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 - 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 - 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 - 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 - 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 - 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 -