TY  - JOUR
A1  - Glebov, Sergei
A1  - Kiselev, Oleg
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Weakly nonlinear dispersive waves under parametric resonance perturbation
N2  - We consider a solution of the nonlinear Klein-Gordon equation perturbed by a parametric driver. The frequency of parametric perturbation varies slowly and passes through a resonant value, which leads to a solution change. We obtain a new connection formula for the asymptotic solution before and after the resonance.
Y1  - 2010
UR  - http://www3.interscience.wiley.com/cgi-bin/issn?DESCRIPTOR=PRINTISSN&VALUE=0022-2526
U6  - https://doi.org/10.1111/j.1467-9590.2009.00460.x
SN  - 0022-2526
ER  - 
TY  - THES
A1  - Hayn, Michael
T1  - Wavelet analysis and spline modeling of geophysical data on the sphere
Y1  - 2010
CY  - Potsdam
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  - JOUR
A1  - Stepanenko, Victor
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - The Cauchy problem for Chaplygin's system
N2  - We discuss the Cauchy problem for the so-called Chaplygin system which often appears in gas, aero- and hydrodynamics. This system can be thought of as a nonlinear analogue of the Cauchy-Riemann system in the plane. We pose Cauchy data on a part of the boundary and apply variational approach to construct a solution to this ill-posed problem. The problem actually gives insight to fundamental questions related to instable problems for nonlinear equations.
Y1  - 2010
UR  - http://www.informaworld.com/openurl?genre=journal&issn=1747-6933
U6  - https://doi.org/10.1080/17476930903394978
SN  - 1747-6933
ER  - 
TY  - JOUR
A1  - Bär, Christian
A1  - Bessa, C. Pacelli
T1  - Stochastic completeness and volume growth
N2  - It was suggested in 1999 that a certain volume growth condition for geodesically complete Riemannian manifolds might imply that the manifold is stochastically complete. This is motivated by a large class of examples and by a known analogous criterion for recurrence of Brownian motion. We show that the suggested implication is not true in general. We also give counterexamples to a converse implication.
Y1  - 2010
UR  - http://www.ams.org/proc/
U6  - https://doi.org/10.1090/S0002-9939-10-10281-0
SN  - 0002-9939
ER  - 
TY  - INPR
A1  - Läuter, Henning
A1  - Ramadan, Ayad
T1  - Statistical Scaling of Categorical Data
N2  - Estimation and testing of distributions in metric spaces are well known. R.A. Fisher, J. Neyman, W. Cochran and M. Bartlett achieved essential results on the statistical analysis of categorical data. In the last 40 years many other statisticians found important results in this field. Often data sets contain categorical data, e.g. levels of factors or names. There does not exist any ordering or any distance between these categories. At each level there are measured some metric or categorical values. We introduce a new method of scaling based on statistical decisions. For this we define empirical probabilities for the original observations and find a class of distributions in a metric space where these empirical probabilities can be found as approximations for equivalently defined probabilities. With this method we identify probabilities connected with the categorical data and probabilities in metric spaces. Here we get a mapping from the levels of factors or names into points of a metric space. This mapping yields the scale for the categorical data. From the statistical point of view we use multivariate statistical methods, we calculate maximum likelihood estimations and compare different approaches for scaling.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2010, 01 
Y1  - 2010
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49566
ER  - 
TY  - THES
A1  - Ramadan, Ayad
T1  - Statistical model for categorical data
Y1  - 2010
CY  - Potsdam
ER  - 
TY  - THES
A1  - Kammanee, Athassawat
T1  - Some inverse potential problems
Y1  - 2010
CY  - Potsdam
ER  - 
TY  - THES
A1  - Pornsawad, Pornsarp
T1  - Solution of nonlinear inverse ill-posed problems via Runge-Kutta methods
Y1  - 2010
CY  - Potsdam
ER  - 
TY  - THES
A1  - Chi, Nguyen Phuong
T1  - Research on improvement of contents and methods of teaching the elements of probability and statistics in teh Vietnamese upper-secondary school
Y1  - 2010
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Geese, Anne
A1  - Mandea, Mioara
A1  - Lesur, Vincent
A1  - Hayn, Michael
T1  - Regional modelling of the Southern African geomagnetic field using harmonic splines
N2  - Over the southern African region the geomagnetic field is weak and changes rapidly. For this area series of geomagnetic field measurements exist since the 1950s. We take advantage of the existing repeat station surveys and observatory annual means, and clean these data sets by eliminating jumps and minimizing external field contributions in the original time-series. This unique data set allows us to obtain a detailed view of the geomagnetic field behaviour in space and time by computing a regional model. For this, we use a system of representation similar to harmonic splines. Initially, the technique is systematically tested on synthetic data. After systematically testing the method on synthetic data, we derive a model for 1961-2001 that gives a detailed view of the fast changes of the geomagnetic field in this region.
Y1  - 2010
UR  - http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1365-246X
U6  - https://doi.org/10.1111/j.1365-246X.2010.04575.x
SN  - 0956-540X
ER  - 
TY  - JOUR
A1  - Hainzl, Sebastian
A1  - Brietzke, Gilbert B.
A1  - Zöller, Gert
T1  - Quantitative earthquake forecasts resulting from static stress triggering
N2  - In recent years, the triggering of earthquakes has been discussed controversially with respect to the underlying mechanisms and the capability to evaluate the resulting seismic hazard. Apart from static stress interactions, other mechanisms including dynamic stress transfer have been proposed to be part of a complex triggering process. Exploiting the theoretical relation between long-term earthquake rates and stressing rate, we demonstrate that static stress changes resulting from an earthquake rupture allow us to predict quantitatively the aftershock activity without tuning specific model parameters. These forecasts are found to be in excellent agreement with all first-order characteristics of aftershocks, in particular, (1) the total number, (2) the power law distance decay, (3) the scaling of the productivity with the main shock magnitude, (4) the foreshock probability, and (5) the empirical Bath law providing the maximum aftershock magnitude, which supports the conclusion that static stress transfer is the major mechanism of earthquake triggering.
Y1  - 2010
UR  - http://www.agu.org/journals/jb/
U6  - https://doi.org/10.1029/2010jb007473
SN  - 0148-0227
ER  - 
TY  - JOUR
A1  - Weiße, Andrea Y.
A1  - Middleton, Richard H.
A1  - Huisinga, Wilhelm
T1  - Quantifying uncertainty, variability and likelihood for ordinary differential equation models
N2  - Background: In many applications, ordinary differential equation (ODE) models are subject to uncertainty or variability in initial conditions and parameters. Both, uncertainty and variability can be quantified in terms of a probability density function on the state and parameter space. Results: The partial differential equation that describes the evolution of this probability density function has a form that is particularly amenable to application of the well- known method of characteristics. The value of the density at some point in time is directly accessible by the solution of the original ODE extended by a single extra dimension (for the value of the density). This leads to simple methods for studying uncertainty, variability and likelihood, with significant advantages over more traditional Monte Carlo and related approaches especially when studying regions with low probability. Conclusions: While such approaches based on the method of characteristics are common practice in other disciplines, their advantages for the study of biological systems have so far remained unrecognized. Several examples illustrate performance and accuracy of the approach and its limitations.
Y1  - 2010
UR  - http://www.biomedcentral.com/1752-0509/
U6  - https://doi.org/10.1186/1752-0509-4-144
SN  - 1752-0509
ER  - 
TY  - JOUR
A1  - Bailey, Iain W.
A1  - Ben-Zion, Yehuda
A1  - Becker, Thorsten W.
A1  - Holschneider, Matthias
T1  - Quantifying focal mechanism heterogeneity for fault zones in central and southern California
N2  - P>We present a statistical analysis of focal mechanism orientations for nine California fault zones with the goal of quantifying variations of fault zone heterogeneity at seismogenic depths. The focal mechanism data are generated from first motion polarities for earthquakes in the time period 1983-2004, magnitude range 0-5, and depth range 0-15 km. Only mechanisms with good quality solutions are used. We define fault zones using 20 km wide rectangles and use summations of normalized potency tensors to describe the distribution of double-couple orientations for each fault zone. Focal mechanism heterogeneity is quantified using two measures computed from the tensors that relate to the scatter in orientations and rotational asymmetry or skewness of the distribution. We illustrate the use of these quantities by showing relative differences in the focal mechanism heterogeneity characteristics for different fault zones. These differences are shown to relate to properties of the fault zone surface traces such that increased scatter correlates with fault trace complexity and rotational asymmetry correlates with the dominant fault trace azimuth. These correlations indicate a link between the long-term evolution of a fault zone over many earthquake cycles and its seismic behaviour over a 20 yr time period. Analysis of the partitioning of San Jacinto fault zone focal mechanisms into different faulting styles further indicates that heterogeneity is dominantly controlled by structural properties of the fault zone, rather than time or magnitude related properties of the seismicity.
Y1  - 2010
UR  - http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1365-246X
U6  - https://doi.org/10.1111/j.1365-246X.2010.04745.x
SN  - 0956-540X
ER  - 
TY  - JOUR
A1  - Garifullinevich, Rustem Nail
A1  - Suleimanov, Bulat Irekovich
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Phase shift in the Whitham zone for the Gurevich-Pitaevskii special solution of the Korteweg-de Vries equation
N2  - We get the leading term of the Gurevich-Pitaevskii special solution of the KdV equation in the oscillation zone without using averaging methods.
Y1  - 2010
UR  - http://www.sciencedirect.com/science/journal/03759601
U6  - https://doi.org/10.1016/j.physleta.2010.01.057
SN  - 0375-9601
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  - BOOK
A1  - Kuxhaus, Olga
T1  - Parametrische Schätzung von elliptischen Copulafunktionen
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Mathematische Statistik un
Y1  - 2010
SN  - 1613-3307
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - THES
A1  - Musunthia, Tiwadee
T1  - On the study of varieties of rings with involution
Y1  - 2010
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Dimitrova, Ilinka
A1  - Koppitz, Jörg
T1  - On some anti-inverse transformation semigroups
N2  - A semigroup S is called anti-inverse if for all a E S there is a b is an element of S such that aba = b and bab = a. Each anti-inverse semigroup is regular. In the present paper, we study anti-inverse subsemigroups within the semigroup T-n of all transformations on an n-element set (1 <= n is an element of N). In particular, we characterize all anti-inverse semigroups within the J-classes of T-n and illustrate our result by four examples.
Y1  - 2010
UR  - http://www.proceedings.bas.bg/
SN  - 1310-1331
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  - Runge, Antonia
T1  - Modellierung der Lebensdauer von Systemen
N2  - Aus dem Inhalt: Einleitung und Zusammenfassung 1 Grundlagen der Lebensdaueranalyse 2 Systemzuverlässigkeit 3 Zensierung 4 Schätzen in nichtparametrischen Modellen 5 Schätzen in parametrischen Modellen 6 Konfidenzintervalle für Parameterschätzungen 7 Verteilung einer gemischten Population 8 Kurze Einführung: Lebensdauer und Belastung 9 Ausblick A R-Quellcode B Symbole und Abkürzungen
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2010, 08 
Y1  - 2010
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-51674
ER  - 
TY  - INPR
A1  - Läuter, Henning
A1  - Ramadan, Ayad
T1  - Modeling and Scaling of Categorical Data
N2  - Estimation and testing of distributions in metric spaces are well known. R.A. Fisher, J. Neyman, W. Cochran and M. Bartlett achieved essential results on the statistical analysis of categorical data. In the last 40 years many other statisticians found important results in this field. Often data sets contain categorical data, e.g. levels of factors or names. There does not exist any ordering or any distance between these categories. At each level there are measured some metric or categorical values. We introduce a new method of scaling based on statistical decisions. For this we define empirical probabilities for the original observations and find a class of distributions in a metric space where these empirical probabilities can be found as approximations for equivalently defined probabilities. With this method we identify probabilities connected with the categorical data and probabilities in metric spaces. Here we get a mapping from the levels of factors or names into points of a metric space. This mapping yields the scale for the categorical data. From the statistical point of view we use multivariate statistical methods, we calculate maximum likelihood estimations and compare different approaches for scaling.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2010, 03 
Y1  - 2010
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49572
ER  - 
TY  - JOUR
A1  - Devchand, Chandrashekar
A1  - Nuyts, Jean
A1  - Weingart, Gregor
T1  - Matryoshka of Special Democratic Forms
N2  - Special p-forms are forms which have components phi_{mu_1...mu_p} equal to +1,-1 or 0 in some orthonormal basis. A p-form phiin Lambda^p R^d is called democratic if the set of nonzero components {phi_{mu_1...mu_p}} is symmetric under the transitive action of a subgroup of O(d,Z) on the indices {1,...,d}. Knowledge of these symmetry groups allows us to define mappings of special democratic p-forms in d dimensions to special democratic P-forms in D dimensions for successively higher P geq p and D geq d. In particular, we display a remarkable nested stucture of special forms including a U(3)-invariant 2-form in six dimensions, a G_2-invariant 3-form in seven dimensions, a Spin(7)- invariant 4-form in eight dimensions and a special democratic 6-form Omega in ten dimensions. The latter has the remarkable property that its contraction with one of five distinct bivectors, yields, in the orthogonal eight dimensions, the Spin(7)-invariant 4-form. We discuss various properties of this ten dimensional form.
Y1  - 2010
UR  - http://www.springerlink.com/content/dn2h0l040x382q07/
SN  - 143-0916
ER  - 
TY  - JOUR
A1  - Gaci, Said
A1  - Zaourar, Naima
A1  - Hamoudi, Mehdi
A1  - Holschneider, Matthias
T1  - Local regularity analysis of strata heterogeneities from sonic logs
N2  - Borehole logs provide geological information about the rocks crossed by the wells. Several properties of rocks can be interpreted in terms of lithology, type and quantity of the fluid filling the pores and fractures. Here, the logs are assumed to be nonhomogeneous Brownian motions (nhBms) which are generalized fractional Brownian motions (fBms) indexed by depth-dependent Hurst parameters H(z). Three techniques, the local wavelet approach (LWA), the average-local wavelet approach (ALWA), and Peltier Algorithm (PA), are suggested to estimate the Hurst functions (or the regularity profiles) from the logs. First, two synthetic sonic logs with different parameters, shaped by the successive random additions (SRA) algorithm, are used to demonstrate the potential of the proposed methods. The obtained Hurst functions are close to the theoretical Hurst functions. Besides, the transitions between the modeled layers are marked by Hurst values discontinuities. It is also shown that PA leads to the best Hurst value estimations. Second, we investigate the multifractional property of sonic logs data recorded at two scientific deep boreholes: the pilot hole VB and the ultra deep main hole HB, drilled for the German Continental Deep Drilling Program (KTB). All the regularity profiles independently obtained for the logs provide a clear correlation with lithology, and from each regularity profile, we derive a similar segmentation in terms of lithological units. The lithological discontinuities (strata' bounds and faults contacts) are located at the local extrema of the Hurst functions. Moreover, the regularity profiles are compared with the KTB estimated porosity logs, showing a significant relation between the local extrema of the Hurst functions and the fluid-filled fractures. The Hurst function may then constitute a tool to characterize underground heterogeneities.
Y1  - 2010
UR  - http://www.copernicus.org/EGU/npg/npg.htm
U6  - https://doi.org/10.5194/npg-17-455-2010
SN  - 1023-5809
ER  - 
TY  - JOUR
A1  - Fradon, Myriam
A1  - Roelly, Sylvie
T1  - Infinitely many Brownian globules with Brownian radii
N2  - We consider an infinite system of non-overlapping globules undergoing Brownian motions in R-3. 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 infinite-dimensional 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.
Y1  - 2010
UR  - http://www.worldscinet.com/sd/sd.shtml
U6  - https://doi.org/10.1142/S021949371000311x
SN  - 0219-4937
ER  - 
TY  - JOUR
A1  - Hainzl, Sebastian
A1  - Zöller, Gert
A1  - Wang, Rongjiang
T1  - Impact of the receiver fault distribution on aftershock activity
N2  - Aftershock models are usually based either on purely empirical relations ignoring the physical mechanism or on deterministic calculations of stress changes on a predefined receiver fault orientation. Here we investigate the effect of considering more realistic fault systems in models based on static Coulomb stress changes. For that purpose, we perform earthquake simulations with elastic half-space stress interactions, rate-and-state dependent frictional earthquake nucleation, and extended ruptures with heterogeneous (fractal) slip distributions. We find that the consideration of earthquake nucleation on multiple receiver fault orientations does not influence the shape of the temporal Omori-type aftershock decay, but changes significantly the predicted spatial patterns and the total number of triggered events. So-called stress shadows with decreased activity almost vanish, and activation decays continuously with increasing distance from the main shock rupture. The total aftershock productivity, which is shown to be almost independent of the assumed background rate, increases significantly if multiple receiver fault planes exist. The application to the 1992 M7.3 Landers, California, aftershock sequence indicates a good agreement with the locations and the total productivity of the observed directly triggered aftershocks.
Y1  - 2010
UR  - http://www.agu.org/journals/jb/
U6  - https://doi.org/10.1029/2008jb006224
SN  - 0148-0227
ER  - 
TY  - THES
A1  - Lekkoksung, Somsak
T1  - Hyperidentities and hypersubstitutions of many-sorted algebras
Y1  - 2010
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Voss, Carola Regine
T1  - Harness-Prozesse
N2  - Harness-Prozesse finden in der Forschung immer mehr Anwendung. Vor allem gewinnen Harness-Prozesse in stetiger Zeit an Bedeutung. Grundlegende Literatur zu diesem Thema ist allerdings wenig vorhanden. In der vorliegenden Arbeit wird die vorhandene Grundlagenliteratur zu Harness-Prozessen in diskreter und stetiger Zeit aufgearbeitet und Beweise ausgeführt, die bisher nur skizziert waren. Ziel dessen ist die Existenz einer Zerlegung von Harness-Prozessen über Z beziehungsweise R+ nachzuweisen.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2010, 13 
Y1  - 2010
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49651
ER  - 
TY  - JOUR
A1  - Shin, Seoleun
A1  - Sommer, Matthias
A1  - Reich, Sebastian
A1  - Névir, Peter
T1  - Evaluation of three spatial discretization schemes with the Galewsky et al. test
N2  - We evaluate the Hamiltonian particle methods (HPM) and the Nambu discretization applied to shallow-water equations on the sphere using the test suggested by Galewsky et al. (2004). Both simulations show excellent conservation of energy and are stable in long-term simulation. We repeat the test also using the ICOSWP scheme to compare with the two conservative spatial discretization schemes. The HPM simulation captures the main features of the reference solution, but wave 5 pattern is dominant in the simulations applied on the ICON grid with relatively low spatial resolutions. Nevertheless, agreement in statistics between the three schemes indicates their qualitatively similar behaviors in the long-term integration.
Y1  - 2010
UR  - http://www3.interscience.wiley.com/cgi-bin/jhome/106562719
U6  - https://doi.org/10.1002/Asl.279
SN  - 1530-261X
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  - BOOK
A1  - Liero, Hannelore
T1  - Estimation and testing the effect of covariates in accelerated life time models under censoring
N2  - The accelerated lifetime model is considered. To test the influence of the covariate we transform the model in a regression model. Since censoring is allowed this approach leads to a goodness-of-fit problem for regression functions under censoring. So nonparametric estimation of regression functions under censoring is investigated, a limit theorem for a L2-distance is stated and a test procedure is formulated. Finally a Monte Carlo procedure is proposed.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2010, 02 
KW  - accelerated life time model
KW  - censoring
KW  - goodness-of-fit testing
KW  - nonparametric regression estimation
KW  - Monte Carlo testing
Y1  - 2010
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-52823
ER  - 
TY  - BOOK
A1  - Liero, Hannelore
T1  - Estimation and testing the effect of covariates in accelerated life time models under censoring
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Mathematische Statistik un
Y1  - 2010
SN  - 1613-3307
PB  - Univ.
CY  - Potsdam
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  - Kunze, Simone
T1  - Das Sammelbilderproblem
N2  - Aus dem Inhalt: 1 Einleitung 2 Entwicklung der Lösungsansätze 3 Martingalansatz 4 Markov-Ketten Ansatz 5 Einbettung in Poisson Prozesse 6 Kombinatorische Ansätze 7 Zusammenfassung und Ausblick Literaturverzeichnis
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2010, 12 
Y1  - 2010
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-51646
ER  - 
TY  - JOUR
A1  - Andersson, Lars
A1  - Metzger, Jan
T1  - Curvature estimates for stable marginally trapped surfaces
N2  - We derive local integral and sup-estimates for the curvature of stable marginally outer trapped surfaces in a sliced space-time. The estimates bound the shear of a marginally outer trapped surface in terms of the intrinsic and extrinsic curvature of a slice containing the surface. These estimates are well adapted to situations of physical interest, such as dynamical horizons.
Y1  - 2010
UR  - http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.jdg
SN  - 0022-040X
ER  - 
TY  - THES
A1  - Pénisson, Sophie
T1  - Conditional limit theorems for multitype branching processes and illustration in epidemiological risk analysis
T1  - Bedingte Grenzwertsätze für Mehrtyp-Verzweigungsprozesse und Illustration in epidemiologischen Risikoanalyse
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 diffusion process. We are interested in different kinds of conditioning on non-extinction, 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 X_t on non-extinction (X_t≠0), or more generally on non-extinction in a near future 0≤θ<∞ (X_{t+θ}≠0), and by letting t tend to infinity. We prove the result, new in the multitype framework and for θ>0, that this limit exists and is non-degenerate. This reflects 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 θ=0. In a second step we study the behavior of the population in case of a very late extinction, obtained as the limit when θ tends to infinity of the process conditioned by X_{t+θ}≠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 X_t is a multitype Feller diffusion process. We investigate the not yet considered case where X_t 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 θ, 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 θ, 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 (X_t|X_t≠0)_t betrachten (oder allgemeiner auf Überleben in naher Zukunft 0≤θ<∞, (X_t|X_{t+θ}≠0)_t). Wir beweisen das Ergebnis, neuartig im mehrtypen Rahmen und für θ>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 θ=0 entspricht). In einem zweiten Schritt studieren wir das Verhalten der Populationen im Falle eines sehr späten Aussterbens, welches wir durch den Grenzübergang auf θ→∞ 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 X_t ein mehrtyp-BGWc Prozess ist und beweisen die Existenz des zugehörigen 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 θ, 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 Schätzer, die an die jeweiligen Stufen der Evolution adaptiert sind (Wachstumsphase, Verfallphase sowie die Verfallphase, wenn das Aussterben sehr spät 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 ermöglichen uns die Betrachtung der Aussterbensphase der Bovinen spongiformen Enzephalopathie Epidemie in Großbritannien. Wir schätzen den Infektionsparameter in Bezug auf mögliche 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.
KW  - Mehrtyp-Verzweigungsprozesse
KW  - Feller Diffusionsprozesse
KW  - Schätzung von Verzweigungsprozessen
KW  - Epidemiologie
KW  - Risikoanalyse
KW  - Multitype branching processes
KW  - Feller diffusion processes
KW  - Estimation for branching processes
KW  - Epidemiology
KW  - Risk analysis
Y1  - 2010
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-45307
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  - 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  - JOUR
A1  - Glebov, Sergei
A1  - Kiselev, Oleg
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Autoresonance in a dissipative system
N2  - We study the autoresonant solution of Duffing's equation in the presence of dissipation. This solution is proved to be an attracting set. We evaluate the maximal amplitude of the autoresonant solution and the time of transition from autoresonant growth of the amplitude to the mode of fast oscillations. Analytical results are illustrated by numerical simulations.
Y1  - 2010
UR  - http://iopscience.iop.org/1751-8121/
U6  - https://doi.org/10.1088/1751-8113/43/21/215203
SN  - 1751-8113
ER  - 
TY  - JOUR
A1  - Bär, Christian
A1  - Pfaeffle, Frank
T1  - Asymptotic heat kernel expansion in the semi-classical limit
N2  - Let H-h = h(2)L + V, where L is a self-adjoint Laplace type operator acting on sections of a vector bundle over a compact Riemannian manifold and V is a symmetric endomorphism field. We derive an asymptotic expansion for the heat kernel of H-h as h SE arrow 0. As a consequence we get an asymptotic expansion for the quantum partition function and we see that it is asymptotic to the classical partition function. Moreover, we show how to bound the quantum partition function for positive h by the classical partition function.
Y1  - 2010
UR  - http://www.springerlink.com/content/100467
U6  - https://doi.org/10.1007/s00220-009-0973-3
SN  - 0010-3616
ER  - 
TY  - THES
A1  - Abed, Jamil
T1  - An iterative approach to operators on manifolds with singularities
T1  - Ein iterativer Zugang zu Operatoren auf Mannigfaltigkeiten mit Singularitäten
N2  - We establish elements of a new approach to ellipticity and parametrices within operator algebras on manifolds with higher singularities, only based on some general axiomatic requirements on parameter-dependent operators in suitable scales of spaes. 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 involves two separate theories, one near the tip of the corner and another one at the conical exit to infinity. However, concerning the conical exit to infinity, we establish here a new concrete calculus of edge-degenerate operators which can be iterated to higher singularities.
N2  - Wir führen einen neuen Zugang ein zu Elliptizität und Parametrices in Operatorenalgebren auf Mannigfaltigkeiten mit höheren Singularitäten, nur basierend auf allgemeinen axiomatischen Voraussetzungen über parameter-abhängige Operatoren in geeigneten Skalen von Räumen. Die Idee besteht darin, ein iteratives Verfahren zu modellieren mit neuen Generationen von parameter-abhängigen Operatortheorien, zusammen mit neuen Skalen von Räumen, die analoge Voraussetzungen erfüllen wie die ursprünglichen Objekte, jetzt auf dem entsprechenden höheren Niveau. Der „volle“ Kalkül besteht aus zwei separaten Theorien, eine nahe der Spitze der Ecke und eine andere am konischen Ausgang nach Unendlich. Allerdings, bezüglich des konischen Ausgangs nach Unendlich, bauen wir hier einen neuen konkreten Kalkül von kanten-entarteten Operatoren auf, der für höhere Singularitäten iteriert werden kann.
KW  - Pseudo-Differentialoperatoren
KW  - kanten- und ecken-entartete Symbole
KW  - Elliptizität
KW  - Parametrices
KW  - höhere Singularitäten
KW  - Pseudo-differential operators
KW  - edge- and corner-degenerate symbols
KW  - ellipticity
KW  - parametrices
KW  - higher singularities
Y1  - 2010
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-44757
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  - JOUR
A1  - Bergemann, Kay
A1  - Reich, Sebastian
T1  - A mollified ensemble Kalman filter
N2  - It is well recognized that discontinuous analysis increments of sequential data assimilation systems, such as ensemble Kalman filters, might lead to spurious high-frequency adjustment processes in the model dynamics. Various methods have been devised to spread out the analysis increments continuously over a fixed time interval centred about the analysis time. Among these techniques are nudging and incremental analysis updates (IAU). Here we propose another alternative, which may be viewed as a hybrid of nudging and IAU and which arises naturally from a recently proposed continuous formulation of the ensemble Kalman analysis step. A new slow-fast extension of the popular Lorenz-96 model is introduced to demonstrate the properties of the proposed mollified ensemble Kalman filter.
Y1  - 2010
UR  - http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1477-870X
U6  - https://doi.org/10.1002/Qj.672
SN  - 0035-9009
ER  - 
TY  - JOUR
A1  - Bergemann, Kay
A1  - Reich, Sebastian
T1  - A localization technique for ensemble Kalman filters
N2  - Ensemble Kalman filter techniques are widely used to assimilate observations into dynamical models. The phase- space dimension is typically much larger than the number of ensemble members, which leads to inaccurate results in the computed covariance matrices. These inaccuracies can lead, among other things, to spurious long-range correlations, which can be eliminated by Schur-product-based localization techniques. In this article, we propose a new technique for implementing such localization techniques within the class of ensemble transform/square-root Kalman filters. Our approach relies on a continuous embedding of the Kalman filter update for the ensemble members, i.e. we state an ordinary differential equation (ODE) with solutions that, over a unit time interval, are equivalent to the Kalman filter update. The ODE formulation forms a gradient system with the observations as a cost functional. Besides localization, the new ODE ensemble formulation should also find useful application in the context of nonlinear observation operators and observations that arrive continuously in time.
Y1  - 2010
UR  - http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1477-870X
U6  - https://doi.org/10.1002/Qj.591
SN  - 0035-9009
ER  -