TY  - INPR
A1  - Prasse, Paul
A1  - Gruben, Gerrit
A1  - Machlika, Lukas
A1  - Pevny, Tomas
A1  - Sofka, Michal
A1  - Scheffer, Tobias
T1  - Malware Detection by HTTPS Traffic Analysis
N2  - In order to evade detection by network-traffic analysis, a growing proportion of malware uses the encrypted HTTPS protocol. We explore the problem of detecting  malware on client computers based on HTTPS traffic analysis. In this setting, malware has to be detected based on the host IP address, ports, timestamp,  and data volume information of TCP/IP packets that are sent and received by all the applications on the client. We develop a scalable protocol that allows us to collect network flows of known malicious and benign applications as training data and derive a malware-detection method based on a neural networks and sequence classification. We study the method's ability to detect known and new, unknown malware in a large-scale empirical study.
KW  - machine learning
KW  - computer security
Y1  - 2017
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-100942
ER  - 
TY  - INPR
A1  - Ly, Ibrahim
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Generalised Beltrami equations
N2  - We enlarge the class of Beltrami equations by developping a stability theory for the sheaf of solutions of an overdetermined elliptic system of first order homogeneous partial differential equations with constant coefficients in the Euclidean space.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 2(2013)14 
KW  - Quasiconformal mapping
KW  - Beltrami equation
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-67416
ER  - 
TY  - INPR
A1  - Roelly, Sylvie
T1  - Reciprocal processes : a stochastic analysis approach
N2  - Reciprocal processes, whose concept can be traced back to E. Schrödinger, form a class of stochastic processes constructed as mixture of bridges, that satisfy a time Markov field property. We discuss here a new unifying approach to characterize several types of reciprocal processes via duality formulae on path spaces: The case of reciprocal processes with continuous paths associated to Brownian diffusions and the case of pure jump reciprocal processes associated to counting processes are treated. This presentation is based on joint works with M. Thieullen, R. Murr and C. Léonard.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 2 (2013) 6 
KW  - Reciprocal process
KW  - Brownian bridge
KW  - Poisson bridge
KW  - duality formula
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-64588
SN  - 2193-6943
ER  - 
TY  - INPR
A1  - Cattiaux, Patrick
A1  - Fradon, Myriam
A1  - Kulik, Alexei Michajlovič
A1  - Roelly, Sylvie
T1  - Long time behavior of stochastic hard ball systems
N2  - We study the long time behavior of a system of two or three Brownian hard balls living in the Euclidean space of dimension at least two, submitted to a mutual attraction and to elastic collisions.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 2(2013)15 
KW  - Stochastic differential equations
KW  - hard core interaction
KW  - reversible measure
KW  - normal reflection
KW  - local time
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-68388
ER  - 
TY  - INPR
A1  - Léonard, Christian
A1  - Roelly, Sylvie
A1  - Zambrini, Jean-Claude
T1  - Temporal symmetry of some classes of stochastic processes
N2  - In this article we analyse the structure of Markov processes and reciprocal processes to underline their time symmetrical properties, and to compare them. Our originality consists in adopting a unifying approach of reciprocal processes, independently of special frameworks in which the theory was developped till now (diffusions, or pure jump processes). This leads to some new results, too.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 2 (2013) 7 
KW  - Markov processes
KW  - reciprocal processes
KW  - time symmetry
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-64599
SN  - 2193-6943
ER  - 
TY  - INPR
A1  - Nehring, Benjamin
A1  - Poghosyan, Suren
A1  - Zessin, Hans
T1  - On the construction of point processes in statistical mechanics
N2  - By means of the cluster expansion method we show that a recent result of Poghosyan and Ueltschi (2009) combined with a result of Nehring (2012) yields a construction of point processes of classical statistical mechanics as well as processes related to the Ginibre Bose gas of Brownian loops and to the dissolution in R^d of Ginibre's Fermi-Dirac gas of such loops. The latter will be identified as a Gibbs perturbation of the ideal Fermi gas. On generalizing these considerations we will obtain the existence of a large class of Gibbs perturbations of the so-called KMM-processes as they were introduced by Nehring (2012). Moreover, it is shown that certain "limiting Gibbs processes" are Gibbs in the sense of Dobrushin, Lanford and Ruelle if the underlying potential is positive. And finally, Gibbs modifications of infinitely divisible point processes are shown to solve a new integration by parts formula if the underlying potential is positive.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 2 (2013) 5 
KW  - Levy measure
KW  - cluster expansion
KW  - Gibbs perturbation
KW  - DLR equation
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-64080
ER  - 
TY  - INPR
A1  - Keller, Peter
T1  - Mathematical modeling of molecular motors
N2  - Amongst the many complex processes taking place in living cells, transport of cargoes across the cytosceleton is fundamental to cell viability and activity. To move cargoes between the different cell parts, cells employ Molecular Motors. The motors operate by transporting cargoes along the so-called cellular micro-tubules, namely rope-like structures that connect, for instance, the cell-nucleus and outer membrane. We introduce a new Markov Chain, the killed Quasi-Random-Walk, for such transport molecules and derive properties like the maximal run length and time. Furthermore we introduce permuted balance, which is a more flexible extension of the ordinary reversibility and introduce the notion of Time Duality, which compares certain passage times pathwise. We give a number of sufficient conditions for Time Duality based on the geometry of the transition graph. Both notions are closely related to properties of the killed Quasi-Random-Walk.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 2 (2013) 1 
KW  - Markov chain
KW  - time duality
KW  - transition path theory
KW  - absorption
KW  - molecular motor
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-63045
ER  - 
TY  - INPR
A1  - Roelly, Sylvie
A1  - Ruszel, Wioletta M.
T1  - Propagation of Gibbsianness for infinite-dimensional diffusions with space-time interaction
N2  - We consider infinite-dimensional diffusions where the interaction between the coordinates has a finite extent both in space and time. In particular, it is not supposed to be smooth or Markov. The initial state of the system is Gibbs, given by a strong summable interaction. If the strongness of this initial interaction is lower than a suitable level, and if the dynamical interaction is bounded from above in a right way, we prove that the law of the diffusion at any time t is a Gibbs measure with absolutely summable interaction. The main tool is a cluster expansion in space uniformly in time of the Girsanov factor coming from the dynamics and exponential ergodicity of the free dynamics to an equilibrium product measure.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 2(2013)18 
KW  - infinite-dimensional diffusion
KW  - cluster expansion
KW  - non-Markov drift
KW  - Girsanov formula
KW  - ultracontractivity
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-69014
ER  - 
TY  - INPR
A1  - Shlapunov, Alexander
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Sturm-Liouville problems in domains with non-smooth edges
N2  - We consider a (generally, non-coercive) mixed boundary value problem in a bounded domain for a second order elliptic differential operator A. The differential operator is assumed to be of divergent form and the boundary operator B is of Robin type. The boundary is assumed to be a Lipschitz surface. Besides, we distinguish a closed subset of the boundary and control the growth of solutions near this set. We prove that the pair (A,B) induces a Fredholm operator L in suitable weighted spaces of Sobolev type, the weight function being a power of the distance to the singular set. Moreover, we prove the completeness of root functions related to L.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 2(2013)13 
KW  - Second order elliptic equations
KW  - non-coercive boundary conditions
KW  - root functions
KW  - weighted spaces
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-67336
ER  - 
TY  - INPR
A1  - Kiselev, Oleg
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - The capture of a particle into resonance at potential hole with dissipative perturbation
N2  - We study the capture of a particle into resonance at a potential hole with dissipative perturbation and periodic outside force. The measure of resonance solutions is evaluated. We also derive an asymptotic formula for the parameter range of those solutions which are captured into resonance.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 2 (2013) 9 
KW  - Capture into resonance
KW  - small parameter
KW  - matching of asymptotic expansions
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-64725
SN  - 2193-6943
ER  - 
TY  - INPR
A1  - Alsaedy, Ammar
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Normally solvable nonlinear boundary value problems
N2  - We study a boundary value problem for an overdetermined elliptic system of nonlinear first order differential equations with linear boundary operators. Such a problem is solvable for a small set of data, and so we pass to its variational formulation which consists in minimising the discrepancy. The Euler-Lagrange equations for the variational problem are far-reaching analogues of the classical Laplace equation. Within the framework of Euler-Lagrange equations we specify an operator on the boundary whose zero set consists precisely of those boundary data for which the initial problem is solvable. The construction of such operator has much in common with that of the familiar Dirichlet to Neumann operator. In the case of linear problems we establish complete results.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 2(2013)11 
KW  - Nonlinear Laplace operator
KW  - boundary value problem
KW  - Dirichlet to Neumann operator
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-65077
SN  - 2193-6943
ER  - 
TY  - INPR
A1  - Murr, Rüdiger
T1  - Characterization of Lévy Processes by a duality formula and related results
N2  - Processes with independent increments are characterized via a duality formula, including Malliavin derivative and difference operators. This result is based on a characterization of infinitely divisible random vectors by a functional equation. A construction of the difference operator by a variational method is introduced and compared to approaches used by other authors for L´evy processes involving the chaos decomposition. Finally we extend our method to characterize infinitely divisible random measures.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2011, 02 
Y1  - 2011
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-43538
ER  - 
TY  - INPR
A1  - Franz, Norbert P.
T1  - Who shot K.G.? : Akunin ermittelt
N2  - Vortrag gehalten auf dem Dritten Internationalen Cechov-Symposium in Badenweiler (Oktober 2004).
Y1  - 2010
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-46364
ER  - 
TY  - INPR
A1  - Siegert, Sabine
T1  - Das Sankt-Petersburg-Paradoxon
N2  - Aus dem Inhalt: 1 Einleitung 2 Historische Lösungsansätze 3 Martingal-Ansatz 4 Markovketten-Ansatz 5 Asymptotische Interpretationen 6 Bezug zur Praxis 7 Résumé Anhang Literaturverzeichnis
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2010, 05 
Y1  - 2010
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49595
ER  - 
TY  - INPR
A1  - Roelly, Sylvie
T1  - Unas propiedades basicas de procesos de ramificación : Lectures held at ICIMAF La Habana, Cuba, 2009 and 2010
N2  - Aus dem Inhalt: 1. Unas propiedades de los procesos de Bienaymé-Galton-Watson de tiempo dis- creto (BGW) 2. Unas propiedades del proceso BGW de tiempo continuo 3. Limites de procesos de BGW cuando la población es numerosa
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2010, 07 
Y1  - 2010
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49620
ER  - 
TY  - INPR
A1  - Pénisson, Sophie
T1  - Estimation of the infection parameter in the different phases of an epidemic modeled by a branching process
N2  - The aim of this paper is to build and compare estimators of the infection parameter in the different phases of an epidemic (growth and extinction phases). The epidemic is modeled by a Markovian process of order d > 1 (allowing non-Markovian life spans), and can be written as a multitype branching process. We propose three estimators suitable for the different classes of criticality of the process, in particular for the subcritical case corresponding to the extinction phase. We prove their consistency and asymptotic normality for two asymptotics, when the number of ancestors (resp. number of generations) tends to infinity. We illustrate the asymptotic properties with simulated examples, and finally use our estimators to study the infection intensity in the extinction phase of the BSE epidemic in Great-Britain.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2010, 04 
Y1  - 2010
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49607
ER  - 
TY  - INPR
A1  - Pénisson, Sophie
T1  - Conditional Limit Theorems for Multitype Branching Processes and Illustration in Epidemiological Risk Analysis
N2  - This thesis is concerned with the issue of extinction of populations composed of different types of individuals, and their behavior before extinction and in case of a very late extinction. We approach this question firstly from a strictly probabilistic viewpoint, and secondly from the standpoint of risk analysis related to the extinction of a particular model of population dynamics. In this context we propose several statistical tools. The population size is modeled by a branching process, which is either a continuous-time multitype Bienaymé-Galton-Watson process (BGWc), or its continuous-state counterpart, the multitype Feller diffsion process. We are interested in different kinds of conditioning on nonextinction, and in the associated equilibrium states. These ways of conditioning have been widely studied in the monotype case. However the literature on multitype processes is much less extensive, and there is no systematic work establishing connections between the results for BGWc processes and those for Feller diffusion processes. In the first part of this thesis, we investigate the behavior of the population before its extinction by conditioning the associated branching process Xt on non-extinction (Xt 6= 0), or more generally on non-extinction in a near future 0 < 1 (Xt+ 0 = 0), and by letting t tend to infinity. We prove the result, new in the multitype framework and for 0 > 0, that this limit exists and is nondegenerate. This re ects a stationary behavior for the dynamics of the population conditioned on non-extinction, and provides a generalization of the so-called Yaglom limit, corresponding to the case 0 = 0. In a second step we study the behavior of the population in case of a very late extinction, obtained as the limit when 0 tends to infinity of the process conditioned by Xt+ 0 = 0. The resulting conditioned process is a known object in the monotype case (sometimes referred to as Q-process), and has also been studied when Xt is a multitype Feller diffusion process. We investigate the not yet considered case where Xt is a multitype BGWc process and prove the existence of the associated Q-process. In addition, we examine its properties, including the asymptotic ones, and propose several interpretations of the process. Finally, we are interested in interchanging the limits in t and 0, as well as in the not yet studied commutativity of these limits with respect to the high-density-type relationship between BGWc processes and Feller processes. We prove an original and exhaustive list of all possible exchanges of limit (long-time limit in t, increasing delay of extinction 0, diffusion limit). The second part of this work is devoted to the risk analysis related both to the extinction of a population and to its very late extinction. We consider a branching population model (arising notably in the epidemiological context) for which a parameter related to the first moments of the offspring distribution is unknown. We build several estimators adapted to different stages of evolution of the population (phase growth, decay phase, and decay phase when extinction is expected very late), and prove moreover their asymptotic properties (consistency, normality). In particular, we build a least squares estimator adapted to the Q-process, allowing a prediction of the population development in the case of a very late extinction. This would correspond to the best or to the worst-case scenario, depending on whether the population is threatened or invasive. These tools enable us to study the extinction phase of the Bovine Spongiform Encephalopathy epidemic in Great Britain, for which we estimate the infection parameter corresponding to a possible source of horizontal infection persisting after the removal in 1988 of the major route of infection (meat and bone meal). This allows us to predict the evolution of the spread of the disease, including the year of extinction, the number of future cases and the number of infected animals. In particular, we produce a very fine analysis of the evolution of the epidemic in the unlikely event of a very late extinction.
N2  - Diese Arbeit befasst sich mit der Frage des Aussterbens von Populationen verschiedener Typen von Individuen. Uns interessiert das Verhalten vor dem Aussterben sowie insbesondere im Falle eines sehr späten Aussterbens. Wir untersuchen diese Fragestellung zum einen von einer rein wahrscheinlichkeitstheoretischen Sicht und zum anderen vom Standpunkt der Risikoanalyse aus, welche im Zusammenhang mit dem Aussterben eines bestimmten Modells der Populationsdynamik steht. In diesem Kontext schlagen wir mehrere statistische Werkzeuge vor. Die Populationsgröße wird entweder durch einen zeitkontinuierlichen mehrtyp-Bienaymé-Galton- Watson Verzweigungsprozess (BGWc) oder durch sein Analogon mit kontinuierlichem Zustandsraum, den Feller Diffusionsprozess, modelliert. Wir interessieren uns für die unterschiedlichen Arten auf Überleben zu bedingen sowie für die hierbei auftretenden Gleichgewichtszustände. Diese Bedingungen wurden bereits weitreichend im Falle eines einzelnen Typen studiert. Im Kontext von mehrtyp-Verzweigungsprozessen hingegen ist die Literatur weniger umfangreich und es gibt keine systematischen Arbeiten, welche die Ergebnisse von BGWc Prozessen mit denen der Feller Diffusionsprozesse verbinden. Wir versuchen hiermit diese Lücke zu schliessen. Im ersten Teil dieser Arbeit untersuchen wir das Verhalten von Populationen vor ihrem Aussterben, indem wir das zeitasymptotysche Verhalten des auf Überleben bedingten zugehörigen Verzweigungsprozesses (Xt / Xt 6= 0)t betrachten (oder allgemeiner auf Überleben in naher Zukunft 0 < 1, (Xt / Xt+ 0 = 0)t). Wir beweisen das Ergebnis, neuartig im mehrtypen Rahmen und für 0 > 0, dass dieser Grenzwert existiert und nicht-degeneriert ist. Dies spiegelt ein stationäres Verhalten für auf Überleben bedingte Bevölkerungsdynamiken wider und liefert eine Verallgemeinerung des sogenannten Yaglom Grenzwertes (welcher dem Fall 0 = 0 entspricht). In einem zweiten Schritt studieren wir das Verhalten der Populationen im Falle eines sehr späten Aussterbens, welches wir durch den Grenzübergang auf 0 > unendlich erhalten. Der resultierende Grenzwertprozess ist ein bekanntes Objekt im eintypen Fall (oftmals als Q-Prozess bezeichnet) und wurde ebenfalls im Fall von mehrtyp-Feller-Diffusionsprozessen studiert. Wir untersuchen den bisher nicht betrachteten Fall, in dem Xt ein mehrtyp-BGWc Prozess ist und beweisen die Existenz des zugeh� origen Q-Prozesses. Darüber hinaus untersuchen wir seine Eigenschaften einschließlich der asymptotischen und weisen auf mehrere Auslegungen hin. Schließlich interessieren wir uns für die Austauschbarkeit der Grenzwerte in t und 0, und die Vertauschbarkeit dieser Grenzwerte in Bezug auf die Beziehung zwischen BGWc und Feller Prozessen. Wir beweisen die Durchführbarkeit aller möglichen Grenzwertvertauschungen (Langzeitverhalten, wachsende Aussterbeverzögerung, Diffusionslimit). Der zweite Teil dieser Arbeit ist der Risikoanalyse in Bezug auf das Aussterben und das sehr späte Aussterben von Populationen gewidmet. Wir untersuchen ein Modell einer verzweigten Bevölkerung (welches vor allem im epidemiologischen Rahmen erscheint), für welche ein Parameter der Reproduktionsverteilung unbekannt ist. Wir konstruieren Sch� atzer, die an die jeweiligen Stufen der Evolution adaptiert sind (Wachstumsphase, Verfallphase sowie die Verfallphase, wenn das Aussterben sehr sp� at erwartet wird), und beweisen zudem deren asymptotische Eigenschaften (Konsistenz, Normalverteiltheit). Im Besonderen bauen wir einen für Q-Prozesse adaptierten kleinste-Quadrate-Schätzer, der eine Vorhersage der Bevölkerungsentwicklung im Fall eines sehr späten Aussterbens erlaubt. Dies entspricht dem Best- oder Worst-Case-Szenario, abhängig davon, ob die Bevölkerung bedroht oder invasiv ist. Diese Instrumente erm� oglichen uns die Betrachtung der Aussterbensphase der Bovinen spongiformen Enzephalopathie Epidemie in Großbritannien. Wir schätzen den Infektionsparameter in Bezug auf m� ogliche bestehende Quellen der horizontalen Infektion nach der Beseitigung des primären Infektionsweges (Tiermehl) im Jahr 1988. Dies ermöglicht uns eine Vorhersage des Verlaufes der Krankheit inklusive des Jahres des Aussterbens, der Anzahl von zukünftigen Fällen sowie der Anzahl infizierter Tiere. Insbesondere ermöglicht es uns die Erstellung einer sehr detaillierten Analyse des Epidemieverlaufs im unwahrscheinlichen Fall eines sehr späten Aussterbens.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2010, 11 
Y1  - 2010
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49589
ER  - 
TY  - INPR
A1  - Kuxhaus, Olga
T1  - Parametrische Schätzungen von elliptischen Copulafunktionen
N2  - Aus dem Inhalt: Inhaltsverzeichnis Abbildungsverzeichnis Tabellenverzeichnis 1 Einleitung und Motivation 2 Multivariate Copulafunktionen 2.1 Einleitung 2.2 Satz von Sklar 2.3 Eigenschaften von Copulafunktionen 3 Abhängigkeitskonzepte 3.1 Lineare Korrelation 3.2 Copulabasierte Abhängigkeitsmaße 3.2.1 Konkordanz 3.2.2 Kendall’s und Spearman’s 3.2.3 Asymptotische Randabhängigkeit 4 Elliptische Copulaklasse 4.1 Sphärische und elliptische Verteilungen 4.2 Normal-Copula 4.3 t-Copula 5 Parametrische Schätzverfahren 5.1 Maximum-Likelihood-Methode 5.1.1 ExakteMaximum-Likelihood-Methode 5.1.2 2-stufige parametrische Maximum-Likelihood-Methode 5.1.3 2-stufige semiparametrische Maximum-Likelihood-Methode 5.2 Momentenmethode 5.3 Kendall’s -Momentenmethode 6 Parameterschätzungen für Normal- und t-Copula 6.1 Normal-Copula 6.1.1 Maximum-Likelihood-Methode 6.1.2 Momentenmethode 6.1.3 Kendall’s Momentenmethode 6.1.4 Spearman’s Momentenmethode 6.2 t-Copula 6.2.1 Verfahren 1 (exakte ML-Methode) 6.2.2 Verfahren 2 (2-stufige rekursive ML-Methode) 6.2.3 Verfahren 3 (2-stufige KM-ML-Methode) 6.2.4 Verfahren 4 (3-stufige M-ML-Methode) 7 Simulationen 7.1 Grundlagen 7.2 Parametrischer Fall 7.3 Nichtparametrischer Fall 7.4 Fazit A Programmausschnitt Literaturverzeichnis
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2010, 09 
Y1  - 2010
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-51681
ER  - 
TY  - INPR
A1  - Nehring, Benjamin
A1  - Zessin, Hans
T1  - A path integral representation of the moment measures of the general ideal Bose gas
N2  - We reconsider the fundamental work of Fichtner ([2]) and exhibit the permanental structure of the ideal Bose gas again, using another approach which combines a characterization of infinitely divisible random measures (due to Kerstan,Kummer and Matthes [5, 6] and Mecke [8, 9]) with a decomposition of the moment measures into its factorial measures due to Krickeberg [4]. To be more precise, we exhibit the moment measures of all orders of the general ideal Bose gas in terms of certain path integrals. This representation can be considered as a point process analogue of the old idea of Symanzik [11] that local times and self-crossings of the Brownian motion can be used as a tool in quantum field theory. Behind the notion of a general ideal Bose gas there is a class of infinitely divisible point processes of all orders with a Levy-measure belonging to some large class of measures containing the one of the classical ideal Bose gas considered by Fichtner. It is well known that the calculation of moments of higher order of point processes are notoriously complicated. See for instance Krickeberg's calculations for the Poisson or the Cox process in [4].
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2010, 10 
Y1  - 2010
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49635
ER  - 
TY  - INPR
A1  - Zessin, Hans
T1  - Classical Symmetric Point Processes : Lectures held at ICIMAF, La Habana, Cuba, 2010
N2  - The aim of these lectures is a reformulation and generalization of the fundamental investigations of Alexander Bach [2, 3] on the concept of probability in the work of Boltzmann [6] in the language of modern point process theory. The dominating point of view here is its subordination under the disintegration theory of Krickeberg [14]. This enables us to make Bach's consideration much more transparent. Moreover the point process formulation turns out to be the natural framework for the applications to quantum mechanical models.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2010, 06 
Y1  - 2010
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49619
ER  - 
TY  - INPR
A1  - Kosman, Admiʾel
T1  - ״הישר והטוב״ - על הלכה ו״מטא-הלכה״ ומשמעותן האקטואלית : ''ועשית הישר והטוב'', דברים ו:יח
T1  - “Right and good” – On Halakha and Meta-Halakha and the actual meaning of these terms today : "And thou shalt do that which is right and good" (Deuteronomy 6:18)
N2  - Der Beitrag setzt sich mit der halachischen Bedeutung von Dtn. 6,18 im Kontext der heutigen Zeit auseinander.
N2  - The article deals with the halakhic importance of Dtn. 6,18 in our times.
KW  - Judentum
KW  - Bibel
KW  - Dtn. 6:18
KW  - Halacha
KW  - Judaism
KW  - Bibel
KW  - Dtn. 6:18
KW  - Halakhah
Y1  - 2010
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-48995
ER  - 
TY  - INPR
A1  - Hovhannisyan, A. H.
A1  - Schulze, Bert-Wolfgang
T1  - On a method for solution of the ordinary differential equations connected with Huygens' equations
T3  - Preprint - (2010) 01 
Y1  - 2010
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-45381
ER  - 
TY  - INPR
A1  - Karp, Lavi
T1  - On the well-posedness of the vacuum Einstein's equations
N2  - The Cauchy problem of the vacuum Einstein's equations aims to find a semimetric g(αβ) of a spacetime with vanishing Ricci curvature Rα,β and prescribed initial data. Under the harmonic gauge condition, the equations Rα,β = 0 are transferred into a system of quasi-linear wave equations which are called the reduced Einstein equations. The initial data for Einstein's equations are a proper Riemannian metric h(αβ) and a second fundamental form K(αβ). A necessary condition for the reduced Einstein equation to satisfy the vacuum equations is that the initial data satisfy Einstein constraint equations. Hence the data (h(αβ),K(αβ)) cannot serve as initial data for the reduced Einstein equations. Previous results in the case of asymptotically flat spacetimes provide a solution to the constraint equations in one type of Sobolev spaces, while initial data for the evolution equations belong to a different type of Sobolev spaces. The goal of our work is to resolve this incompatibility and to show that under the harmonic gauge the vacuum Einstein equations are well-posed in one type of Sobolev spaces.
T3  - Preprint - (2009) 06 
Y1  - 2009
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-36593
ER  - 
TY  - INPR
A1  - Fradon, Myriam
A1  - Roelly, Sylvie
T1  - Infinitely many Brownian globules with Brownian radii
N2  - We consider an infinite system of non overlaping globules undergoing Brownian motions in R3. The term globules means that the objects we are dealing with are spherical, but with a radius which is random and time-dependent. The dynamics is modelized by an infinitedimensional Stochastic Differential Equation with local time. Existence and uniqueness of a strong solution is proven for such an equation with fixed deterministic initial condition. We also find a class of reversible measures.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2009, 07 
Y1  - 2009
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49552
ER  - 
TY  - INPR
A1  - Arnold, Holger
T1  - A linearized DPLL calculus with clause learning (2nd, revised version)
N2  - Many formal descriptions of DPLL-based SAT algorithms either do not include all essential proof techniques applied by modern SAT solvers or are bound to particular heuristics or data structures. This makes it difficult to analyze proof-theoretic properties or the search complexity of these algorithms. In this paper we try to improve this situation by developing a nondeterministic proof calculus that models the functioning of SAT algorithms based on the DPLL calculus with clause learning. This calculus is independent of implementation details yet precise enough to enable a formal analysis of realistic DPLL-based SAT algorithms.
N2  - Viele formale Beschreibungen DPLL-basierter SAT-Algorithmen enthalten entweder nicht alle wesentlichen Beweistechniken, die in modernen SAT-Solvern implementiert sind, oder sind an bestimmte Heuristiken oder Datenstrukturen gebunden. Dies erschwert die Analyse beweistheoretischer Eigenschaften oder der Suchkomplexität derartiger Algorithmen. Mit diesem Artikel versuchen wir, diese Situation durch die Entwicklung eines nichtdeterministischen Beweiskalküls zu verbessern, der die Arbeitsweise von auf dem DPLL-Kalkül basierenden SAT-Algorithmen mit Klausellernen modelliert. Dieser Kalkül ist unabhängig von Implementierungsdetails, aber dennoch präzise genug, um eine formale Analyse realistischer DPLL-basierter SAT-Algorithmen zu ermöglichen.
KW  - Automatisches Beweisen
KW  - Logikkalkül
KW  - SAT
KW  - DPLL
KW  - Klausellernen
KW  - automated theorem proving
KW  - logical calculus
KW  - SAT
KW  - DPLL
KW  - clause learning
Y1  - 2009
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-29080
ER  - 
TY  - INPR
A1  - Louis, Pierre-Yves
A1  - Rouquier, Jean-Baptiste
T1  - Time-to-Coalescence for interacting particle systems : parallel versus sequential updating
N2  - Studying the influence of the updating scheme for MCMC algorithm on spatially extended models is a well known problem. For discrete-time interacting particle systems we study through simulations the effectiveness of a synchronous updating scheme versus the usual sequential one. We compare the speed of convergence of the associated Markov chains from the point of view of the time-to-coalescence arising in the coupling-from-the-past algorithm. Unlike the intuition, the synchronous updating scheme is not always the best one. The distribution of the time-to-coalescence for these spatially extended models is studied too.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2009, 03 
Y1  - 2009
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49454
ER  - 
TY  - INPR
A1  - Rafler, Mathias
T1  - Gaussian loop- and polya processes : a point process approach
N2  - Zufällige Punktprozesse beschreiben eine (zufällige) zeitliche Abfolge von Ereignissen oder eine (zufällige) räumliche Anordnung von Objekten. Deren wichtigster Vertreter ist der Poissonprozess. Der Poissonprozess zum Intensitätsmaß, das Lebesgue-Maß ordnet jedem Gebiet sein Volumen zu, erzeugt lokal, d.h in einem beschränkten Gebiet B, gerade eine mit dem Volumen von B poissonverteilte Anzahl von Punkten, die identisch und unabhängig voneinander in B plaziert werden; im Mittel ist diese Anzahl (B). Ersetzt man durch ein Vielfaches a, so wird diese Anzahl mit dem a-fachen Mittelwert erzeugt. Poissonprozesse, die im gesamten Raum unendlich viele Punkte realisieren, enthalten bereits in einer einzigen Stichprobe genügend Informationen, um Statistik betreiben zu können: Bedingt man lokal bzgl. der Anzahl der Teilchen einer Stichprobe, so fragt man nach allen Punktprozessen, die eine solche Beobachtung hätten liefern können. Diese sind Limespunktprozesse zu dieser Beobachtung. Kommt mehr als einer in Frage, spricht man von einem Phasenübergang. Da die Menge dieser Limespunktprozesse konvex ist, fragt man nach deren Extremalpunkten, dem Rand. Im ersten Teil wird ein Poissonprozess für ein physikalisches Teilchenmodell für Bosonen konstruiert. Dieses erzeugt sogenannte Loops, das sind geschlossene Polygonzüge, die dadurch charakterisiert sind, dass man an einem Ort mit einem Punkt startet, den mit einem normalverteilten Schritt läuft und dabei nach einer gegebenen, aber zufälligen Anzahl von Schritten zum Ausgangspunkt zurückkehrt. Für verschiedene Beobachtungen von Stichproben werden zugehörige Limespunktprozesse diskutiert. Diese Beobachtungen umfassen etwa das Zählen der Loops gemäaß ihrer Länge, das Zählen der Loops insgesamt, oder das Zählen der von den Loops gemachten Schritte. Jede Wahl zieht eine charakteristische Struktur der invarianten Punktprozesse nach sich. In allen hiesigen Fällen wird ein charakteristischer Phasenübergang gezeigt und Extremalpunkte werden als spezielle Poissonprozesse identifiziert. Insbesondere wird gezeigt, wie die Wahl der Beobachtung die Länge der Loops beeinflusst. Geometrische Eigenschaften dieser Poissonprozesse sind der Gegenstand des zweiten Teils der Arbeit. Die Technik der Palmschen Verteilungen eines Punktprozesses erlaubt es, unter den unendlich vielen Loops einer Realisierung den typischen Loop herauszupicken, dessen Geometrie dann untersucht wird. Eigenschaften sind unter anderem die euklidische Länge eines Schrittes oder, nimmt man mehrere aufeinander folgende Schritte, das Volumen des von ihnen definierten Simplex. Weiterhin wird gezeigt, dass der Schwerpunkt eines typischen Loops normalverteilt ist mit einer festen Varianz. Der dritte und letzte Teil befasst sich mit der Konstruktion, den Eigenschaften und der Statistik eines neuartigen Punktprozesses, der Polyascher Summenprozess genannt wird. Seine Konstruktion verallgemeinert das Prinzip der Polyaschen Urne: Im Gegensatz zum Poissonprozess, der alle Punkte unabhängig und vor allem identisch verteilt, werden hier die Punkte nacheinander derart verteilt, dass der Ort, an dem ein Punkt plaziert wird, eine Belohnung auf die Wahrscheinlichkeit bekommt, nach der nachfolgende Punkte verteilt werden. Auf diese Weise baut der Polyasche Summenprozess "Türmchen", indem sich verschiedene Punkte am selben Ort stapeln. Es wird gezeigt, dass dennoch grundlegende Eigenschaften mit denjenigen des Poissonprozesses übereinstimmen, dazu gehören unendliche Teilbarkeit sowie Unabhängigkeit der Zuwächse. Zudem werden sein Laplace-Funktional sowie seine Palmsche Verteilung bestimmt. Letztere zeigt, dass die Höhe der Türmchen gerade geometrisch verteilt ist. Abschließend werden wiederum Statistiken, nun für den Summenprozess, diskutiert. Je nach Art der Beobachtung von der Stichprobe, etwa Anzahl, Gesamthöhe der Türmchen oder beides, gibt es in jedem der drei Fälle charakteristische Limespunktprozesse und es stellt sich heraus, dass die zugehörigen Extremalverteilungen wiederum Polyasche Summenprozesse sind.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2009, 05 
Y1  - 2009
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-51638
ER  - 
TY  - INPR
A1  - Pénisson, Sophie
T1  - Continuous-time multitype branching processes conditioned on very late extinction
N2  - Multitype branching processes and Feller diffusion processes are conditioned on very late extinction. The conditioned laws are expressed as Doob h-transforms of the unconditioned laws, and an interpretation of the conditioned paths for the branching process is given, via the immortal particle. We study different limits for the conditioned process (increasing delay of extinction, long-time behavior, scaling limit) and provide an exhaustive list of exchangeability results.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2009, 06 
Y1  - 2009
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49548
ER  - 
TY  - INPR
A1  - Anders, Martin
T1  - Martingale, Amarts und das starke Gesetz der Grossen Zahlen
N2  - Aus dem Inhalt: Einleitung Kapitel 1. Starke Gesetze der Grossen Zahlen 1. SGGZ unter Wachstumsbedingungen an die p-ten Momente 2. SGGZ für identisch verteilte Zufallsvariablen 3. SGGZ für Prozesse mit *-mixing-Eigenschaft Kapitel 2. Einführung zu diskreten (Sub-,Super-)Martingalen 1. Vorhersagbarkeit 2. gestoppte (Sub-,Super-)Martingale 3. Upcrossings 4. Konvergenzsätze 5. Doob-Zerlegung 6. Eine äquivalente Definition eines (Sub-)Martingals Kapitel 3. Martingale und gleichgradige Integrierbarkeit 1. Gleichmäßige(-f¨ormige,-gradige) Integrierbarkeit 2. gleichgradig integrierbare Martingale Kapitel 4. Martingale und das SGGZ Kapitel 5.”reversed“ (Sub-,Super-)Martingale 1. Konvergenzsätze Kapitel 6. (Sub-,Super-)Martingale mit gerichteter Indexmenge 1. Äquivalente Formulierung eines (Sub-)Martingals 2. Konvergenzsätze Kapitel 7. Quasimartingale,Amarts und Semiamarts 1. Konvergenzsätze 2. Riesz-Zerlegung 3. Doob-Zerlegung Kapitel 8. Amarts und das SGGZ Kapitel 9.”reversed“ Amarts und Semiamarts 1. Konvergenzsätze 2.”Aufwärts“- gegen ”Abwärts“-Adaptiertheit 3. Riesz-Zerlegung 4. Stabilitätsanalyse Kapitel 10. Amarts mit gerichteter Indexmenge 1. Konvergenzsätze 2. Riesz-Zerlegung Anhang A. zur Existenz einer Folge unabhängiger Zufallsvariablen B. Konvergenz
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2009, 01 
Y1  - 2009
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49494
ER  - 
TY  - INPR
A1  - Redig, Frank
A1  - Roelly, Sylvie
A1  - Ruszel, Wioletta
T1  - Short-time Gibbsianness for infinite-dimensional diffusions with space-time interaction
N2  - We consider a class of infinite-dimensional diffusions where the interaction between the components is both spatial and temporal. We start the system from a Gibbs measure with finiterange uniformly bounded interaction. Under suitable conditions on the drift, we prove that there exists t0 > 0 such that the distribution at time t = t0 is a Gibbs measure with absolutely summable interaction. The main tool is a cluster expansion of both the initial interaction and certain time-reversed Girsanov factors coming from the dynamics.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2009, 04 
Y1  - 2009
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49514
ER  - 
TY  - INPR
A1  - Abed, Jamil
A1  - Schulze, Bert-Wolfgang
T1  - Edge-degenerate families of ΨDO’s on an infinite cylinder
N2  - We establish a parameter-dependent pseudo-differential calculus on an infinite cylinder, regarded as a manifold with conical exits to infinity. The parameters are involved in edge-degenerate form, and we formulate the operators in terms of operator-valued amplitude functions.
T3  - Preprint - (2009) 01 
KW  - Edge-degenerate operators
KW  - parameter-dependent pseudodifferential operators
KW  - norm estimates with respect to a parameter
Y1  - 2009
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30365
ER  - 
TY  - INPR
A1  - Schulze, Bert-Wolfgang
T1  - Boundary value problems with the transmission property
N2  - We give a survey on the calculus of (pseudo-differential) boundary value problems with the transmision property at the boundary, and ellipticity in the Shapiro-Lopatinskij sense. Apart from the original results of the work of Boutet de Monvel we present an approach based on the ideas of the edge calculus. In a final section we introduce symbols with the anti-transmission property.
T3  - Preprint - (2009) 03 
Y1  - 2009
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30377
ER  - 
TY  - INPR
A1  - Ma, L.
A1  - Schulze, Bert-Wolfgang
T1  - Operators on manifolds with conical singularities
N2  - We construct elliptic elements in the algebra of (classical pseudo-differential) operators on a manifold M with conical singularities. The ellipticity of any such operator A refers to a pair of principal symbols (σ0, σ1) where σ0 is the standard (degenerate) homogeneous principal symbol, and σ1 is the so-called conormal symbol, depending on the complex Mellin covariable z. The conormal symbol, responsible for the conical singularity, is operator-valued and acts in Sobolev spaces on the base X of the cone. The σ1-ellipticity is a bijectivity condition for all z of real part (n + 1)/2 − γ, n = dimX, for some weight γ. In general, we have to rule out a discrete set of exceptional weights that depends on A. We show that for every operator A which is elliptic with respect to σ0, and for any real weight γ there is a smoothing Mellin operator F in the cone algebra such that A + F is elliptic including σ1. Moreover, we apply the results to ellipticity and index of (operator-valued) edge symbols from the calculus on manifolds with edges.
T3  - Preprint - (2009) 07 
KW  - Operators on manifolds with conical singularities
KW  - conormal symbols
KW  - ellipticity of cone operators
Y1  - 2009
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-36608
ER  - 
TY  - INPR
A1  - Chen, Hua
A1  - Li, Jun-Feng
A1  - Liu, Wei-An
T1  - Behavior of the solution to a chemotaxis model with reproduction term
N2  - Contents: 1 Introduction 2 Global existence and blow-up or quenching of the solution 3 Detailed asymptotical behavior of the solution
T3  - Preprint - (2008) 02 
Y1  - 2008
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30304
ER  - 
TY  - INPR
A1  - Tepoyan, Liparit
T1  - The mixed problem for a degenerate operator equation
N2  - We consider a mixed problem for a degenerate differentialoperator equation of higher order. We establish some embedding theorems in weighted Sobolev spaces and show existence and uniqueness of the generalized solution of this problem. We also give a description of the spectrum for the corresponding operator.
T3  - Preprint - (2008) 06 
Y1  - 2008
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30334
ER  - 
TY  - INPR
A1  - Brauer, Uwe
A1  - Karp, Lavi
T1  - Well-posedness of Einstein-Euler systems in asymptotically flat spacetimes
N2  - We prove a local in time existence and uniqueness theorem of classical solutions of the coupled Einstein{Euler system, and therefore establish the well posedness of this system. We use the condition that the energy density might vanish or tends to zero at infinity and that the pressure is a certain function of the energy density, conditions which are used to describe simplified stellar models. In order to achieve our goals we are enforced, by the complexity of the problem, to deal with these equations in a new type of weighted Sobolev spaces of fractional order. Beside their construction, we develop tools for PDEs and techniques for hyperbolic and elliptic equations in these spaces. The well posedness is obtained in these spaces.
T3  - Preprint - (2008) 07 
Y1  - 2008
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30347
ER  - 
TY  - INPR
A1  - Abed, Jamil
A1  - Schulze, Bert-Wolfgang
T1  - Operators with corner-degenerate symbols
N2  - We establish elements of a new approch to ellipticity and parametrices within operator algebras on a manifold with higher singularities, only based on some general axiomatic requirements on parameter-dependent operators in suitable scales of spaces. The idea is to model an iterative process with new generations of parameter-dependent operator theories, together with new scales of spaces that satisfy analogous requirements as the original ones, now on a corresponding higher level. The “full” calculus is voluminous; so we content ourselves here with some typical aspects such as symbols in terms of order reducing families, classes of relevant examples, and operators near the conical exit to infinity.
T3  - Preprint - (2008) 01 
Y1  - 2008
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30299
ER  - 
TY  - INPR
A1  - Schulze, Bert-Wolfgang
T1  - The iterative structure of corner operators
N2  - We give a brief survey on some new developments on elliptic operators on manifolds with polyhedral singularities. The material essentially corresponds to a talk given by the author during the Conference “Elliptic and Hyperbolic Equations on Singular Spaces”, October 27 - 31, 2008, at the MSRI, University of Berkeley.
T3  - Preprint - (2008) 08 
KW  - Categories of stratified spaces
KW  - ellipticity of corners operators
KW  - principal symbolic hierarchies
KW  - boundary value problems
Y1  - 2008
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30353
ER  - 
TY  - INPR
A1  - Schulze, Bert-Wolfgang
A1  - Wei, Y.
T1  - Edge-boundary problems with singular trace conditions
N2  - The ellipticity of boundary value problems on a smooth manifold with boundary relies on a two-component principal symbolic structure (σψ; σ∂), consisting of interior and boundary symbols. In the case of a smooth edge on manifolds with boundary we have a third symbolic component, namely the edge symbol σ∧, referring to extra conditions on the edge, analogously as boundary conditions. Apart from such conditions in integral form' there may exist singular trace conditions, investigated in [6] on closed' manifolds with edge. Here we concentrate on the phenomena in combination with boundary conditions and edge problem.
T3  - Preprint - (2008) 04 
Y1  - 2008
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30317
ER  - 
TY  - INPR
A1  - Schulze, Bert-Wolfgang
T1  - On a paper of Krupchyk, Tarkhanov, and Tuomela
T3  - Preprint - (2008) 05 
Y1  - 2008
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30325
ER  - 
TY  - INPR
A1  - Champagnat, Nicolas
A1  - Roelly, Sylvie
T1  - Limit theorems for conditioned multitype Dawson-Watanabe processes
N2  - A multitype Dawson-Watanabe process is conditioned, in subcritical and critical cases, on non-extinction in the remote future. On every nite time interval, its distribution law is absolutely continuous with respect to the law of the unconditioned process. A martingale problem characterization is also given. The explicit form of the Laplace functional of the conditioned process is used to obtain several results on the long time behaviour of the mass of the conditioned and unconditioned processes. The general case is considered first, where the mutation matrix which modelizes the interaction between the types, is irreducible. Several two-type models with decomposable mutation matrices are also analysed.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2007, 01 
Y1  - 2007
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49426
ER  - 
TY  - INPR
A1  - Cattiaux, Patrick
A1  - Dai Pra, Paolo
A1  - Poelly, Sylvie
T1  - A constructive approach to a class of ergodic HJB equations with nonsmooth cost
N2  - We consider a class of ergodic Hamilton-Jacobi-Bellman (HJB) equations, related to large time asymptotics of non-smooth multiplicative functional of difusion processes. Under suitable ergodicity assumptions on the underlying difusion, we show existence of these asymptotics, and that they solve the related HJB equation in the viscosity sense.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2007, 02 
Y1  - 2007
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49430
ER  - 
TY  - INPR
A1  - Shlapunov, Alexander
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Formal Poincaré lemma
N2  - We show how the multiple application of the formal Cauchy-Kovalevskaya theorem leads to the main result of the formal theory of overdetermined systems of partial differential equations. Namely, any sufficiently regular system Au = f with smooth coefficients on an open set U ⊂ Rn admits a solution in smooth sections of a bundle of formal power series, provided that f satisfies a compatibility condition in U.
T3  - Preprint - (2007) 02 
Y1  - 2007
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30231
ER  - 
TY  - INPR
A1  - Chen, Hua
A1  - Li, Ke
T1  - The existence and regularity of multiple solutions for a class of infinitely degenerate elliptic equations
N2  - Let X = (X1,.....,Xm) be an infinitely degenerate system of vector fields, we study the existence and regularity of multiple solutions of Dirichelt problem for a class of semi-linear infinitely degenerate elliptic operators associated with the sum of square operator Δx = ∑m(j=1) Xj* Xj.
T3  - Preprint - (2007) 03 
KW  - degenerate elliptic equations
KW  - Logarithmic Sobolev inequality
Y1  - 2007
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30247
ER  - 
TY  - INPR
A1  - Yagdjian, Karen
A1  - Galstian, Anahit
T1  - Fundamental solutions for wave equation in de Sitter model of universe
N2  - In this article we construct the fundamental solutions for the wave equation arising in the de Sitter model of the universe. We use the fundamental solutions to represent solutions of the Cauchy problem and to prove the Lp − Lq-decay estimates for the solutions of the equation with and without a source term.
T3  - Preprint - (2007) 06 
KW  - de Sitter model ; Fundamental solutions ; Decay estimates
Y1  - 2007
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30271
ER  - 
TY  - INPR
A1  - Chen, Hua
A1  - Li, Wei-Xi
A1  - Xu, Chao-Jiang
T1  - Gevrey hypoellipticity for linear and non-linear Fokker-Planck equations
N2  - This paper studies the Gevrey regularity of weak solutions of a class of linear and semilinear Fokker-Planck equations.
T3  - Preprint - (2007) 07 
Y1  - 2007
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30283
ER  - 
TY  - INPR
A1  - Yin, Yang
A1  - Hua, Chen
T1  - On chemotaxis systems with saturation growth
N2  - In this paper, we discuss the global existence of solutions for Chemotaxis models with saturation growth. If the coe±cients of the equations are all positive smooth T-periodic functions, then the problem has a positive T-periodic solution, and meanwhile we discuss here the stability problems for the T-periodic solutions.
T3  - Preprint - (2007) 04 
KW  - Saturation model
KW  - Chemotaxis
KW  - global solution
KW  - asymptotic stable
Y1  - 2007
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30254
ER  - 
TY  - INPR
A1  - Flad, Heinz-Jürgen
A1  - Schneider, Reinhold
A1  - Schulze, Bert-Wolfgang
T1  - Asymptotic regularity of solutions of Hartree-Fock equations with coulomb potential
N2  - We study the asymptotic regularity of solutions of Hartree-Fock equations for Coulomb systems. In order to deal with singular Coulomb potentials, Fock operators are discussed within the calculus of pseudo-differential operators on conical manifolds. First, the non-self-consistent-field case is considered which means that the functions that enter into the nonlinear terms are not the eigenfunctions of the Fock operator itself. We introduce asymptotic regularity conditions on the functions that build up the Fock operator which guarantee ellipticity for the local part of the Fock operator on the open stretched cone R+ × S². This proves existence of a parametrix with a corresponding smoothing remainder from which it follows, via a bootstrap argument, that the eigenfunctions of the Fock operator again satisfy asymptotic regularity conditions. Using a fixed-point approach based on Cances and Le Bris analysis of the level-shifting algorithm, we show via another bootstrap argument, that the corresponding self-consistent-field solutions of the Hartree-Fock equation have the same type of asymptotic regularity.
T3  - Preprint - (2007) 05 
Y1  - 2007
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30268
ER  - 
TY  - INPR
A1  - Liero, Hannelore
A1  - Liero, Matthias
T1  - Testing the acceleration function in life time models
N2  - The accelerated life time model is considered. First, test procedures for testing the parameter of a parametric acceleration function is investigated; this is done under the assumption of parametric and nonparametric baseline distribution. Further, based on nonparametric estimators for regression functions tests are proposed for checking whether a parametric acceleration function is appropriate to model the influence of the covariates. Resampling procedures are discussed for the realization of these methods. Simulations complete the considerations.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2006, 03 
Y1  - 2006
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49405
ER  - 
TY  - INPR
A1  - Läuter, Henning
T1  - On approximate likelihood in survival models
N2  - We give a common frame for different estimates in survival models. For models with nuisance parameters we approximate the profile likelihood and find estimates especially for the proportional hazard model.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2006, 04 
KW  - Approximate likelihood
KW  - profile likelihood
KW  - propor-tional hazard mode
Y1  - 2006
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-51615
ER  -