@unpublished{Murr2011,
  author    = {Murr, R{\"u}diger},
  title     = {Characterization of L{\´e}vy Processes by a duality formula and related results},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-43538},
  year      = {2011},
  abstract  = {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.},
  language  = {en}
}
@unpublished{MeleardRoelly2011,
  author    = {M{\´e}l{\´e}ard, Sylvie and Roelly, Sylvie},
  title     = {A host-parasite multilevel interacting process and continuous approximations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51694},
  year      = {2011},
  abstract  = {We are interested in modeling some two-level population dynamics, resulting from the interplay of ecological interactions and phenotypic variation of individuals (or hosts) and the evolution of cells (or parasites) of two types living in these individuals. The ecological parameters of the individual dynamics depend on the number of cells of each type contained by the individual and the cell dynamics depends on the trait of the invaded individual. Our models are rooted in the microscopic description of a random (discrete) population of individuals characterized by one or several adaptive traits and cells characterized by their type. The population is modeled as a stochastic point process whose generator captures the probabilistic dynamics over continuous time of birth, mutation and death for individuals and birth and death for cells. The interaction between individuals (resp. between cells) is described by a competition between individual traits (resp. between cell types). We look for tractable large population approximations. By combining various scalings on population size, birth and death rates and mutation step, the single microscopic model is shown to lead to contrasting nonlinear macroscopic limits of different nature: deterministic approximations, in the form of ordinary, integro- or partial differential equations, or probabilistic ones, like stochastic partial differential equations or superprocesses. The study of the long time behavior of these processes seems very hard and we only develop some simple cases enlightening the difficulties involved.},
  language  = {en}
}
@unpublished{Voss2010,
  author    = {Voss, Carola Regine},
  title     = {Harness-Prozesse},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49651},
  year      = {2010},
  abstract  = {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 ausgef{\"u}hrt, die bisher nur skizziert waren. Ziel dessen ist die Existenz einer Zerlegung von Harness-Prozessen {\"u}ber Z beziehungsweise R+ nachzuweisen.},
  language  = {de}
}
@unpublished{Kunze2010,
  author    = {Kunze, Simone},
  title     = {Das Sammelbilderproblem},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51646},
  year      = {2010},
  abstract  = {Aus dem Inhalt: 1 Einleitung 2 Entwicklung der L{\"o}sungsans{\"a}tze 3 Martingalansatz 4 Markov-Ketten Ansatz 5 Einbettung in Poisson Prozesse 6 Kombinatorische Ans{\"a}tze 7 Zusammenfassung und Ausblick Literaturverzeichnis},
  language  = {de}
}
@unpublished{Penisson2010,
  author    = {P{\´e}nisson, Sophie},
  title     = {Conditional Limit Theorems for Multitype Branching Processes and Illustration in Epidemiological Risk Analysis},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49589},
  year      = {2010},
  abstract  = {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 Bienaym{\´e}-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.},
  language  = {en}
}
@unpublished{NehringZessin2010,
  author    = {Nehring, Benjamin and Zessin, Hans},
  title     = {A path integral representation of the moment measures of the general ideal Bose gas},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49635},
  year      = {2010},
  abstract  = {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].},
  language  = {en}
}
@unpublished{Kuxhaus2010,
  author    = {Kuxhaus, Olga},
  title     = {Parametrische Sch{\"a}tzungen von elliptischen Copulafunktionen},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51681},
  year      = {2010},
  abstract  = {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 Abh{\"a}ngigkeitskonzepte 3.1 Lineare Korrelation 3.2 Copulabasierte Abh{\"a}ngigkeitsmaße 3.2.1 Konkordanz 3.2.2 Kendall's und Spearman's 3.2.3 Asymptotische Randabh{\"a}ngigkeit 4 Elliptische Copulaklasse 4.1 Sph{\"a}rische und elliptische Verteilungen 4.2 Normal-Copula 4.3 t-Copula 5 Parametrische Sch{\"a}tzverfahren 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 Parametersch{\"a}tzungen f{\"u}r 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},
  language  = {de}
}
@unpublished{Runge2010,
  author    = {Runge, Antonia},
  title     = {Modellierung der Lebensdauer von Systemen},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51674},
  year      = {2010},
  abstract  = {Aus dem Inhalt: Einleitung und Zusammenfassung 1 Grundlagen der Lebensdaueranalyse 2 Systemzuverl{\"a}ssigkeit 3 Zensierung 4 Sch{\"a}tzen in nichtparametrischen Modellen 5 Sch{\"a}tzen in parametrischen Modellen 6 Konfidenzintervalle f{\"u}r Parametersch{\"a}tzungen 7 Verteilung einer gemischten Population 8 Kurze Einf{\"u}hrung: Lebensdauer und Belastung 9 Ausblick A R-Quellcode B Symbole und Abk{\"u}rzungen},
  language  = {de}
}
@unpublished{Roelly2010,
  author    = {Roelly, Sylvie},
  title     = {Unas propiedades basicas de procesos de ramificaci{\´o}n : Lectures held at ICIMAF La Habana, Cuba, 2009 and 2010},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49620},
  year      = {2010},
  abstract  = {Aus dem Inhalt: 1. Unas propiedades de los procesos de Bienaym{\´e}-Galton-Watson de tiempo dis- creto (BGW) 2. Unas propiedades del proceso BGW de tiempo continuo 3. Limites de procesos de BGW cuando la poblaci{\´o}n es numerosa},
  language  = {mul}
}
@unpublished{Zessin2010,
  author    = {Zessin, Hans},
  title     = {Classical Symmetric Point Processes : Lectures held at ICIMAF, La Habana, Cuba, 2010},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49619},
  year      = {2010},
  abstract  = {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.},
  language  = {en}
}
@unpublished{Siegert2010,
  author    = {Siegert, Sabine},
  title     = {Das Sankt-Petersburg-Paradoxon},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49595},
  year      = {2010},
  abstract  = {Aus dem Inhalt: 1 Einleitung 2 Historische L{\"o}sungsans{\"a}tze 3 Martingal-Ansatz 4 Markovketten-Ansatz 5 Asymptotische Interpretationen 6 Bezug zur Praxis 7 R{\´e}sum{\´e} Anhang Literaturverzeichnis},
  language  = {de}
}
@unpublished{Penisson2010,
  author    = {P{\´e}nisson, Sophie},
  title     = {Estimation of the infection parameter in the different phases of an epidemic modeled by a branching process},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49607},
  year      = {2010},
  abstract  = {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.},
  language  = {en}
}
@unpublished{LaeuterRamadan2010,
  author    = {L{\"a}uter, Henning and Ramadan, Ayad},
  title     = {Modeling and Scaling of Categorical Data},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49572},
  year      = {2010},
  abstract  = {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.},
  language  = {de}
}
@book{Liero2010,
  author    = {Liero, Hannelore},
  title     = {Estimation and testing the effect of covariates in accelerated life time models under censoring},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-52823},
  publisher      = {Universit{\"a}t Potsdam},
  year      = {2010},
  abstract  = {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.},
  language  = {en}
}
@unpublished{LaeuterRamadan2010,
  author    = {L{\"a}uter, Henning and Ramadan, Ayad},
  title     = {Statistical Scaling of Categorical Data},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49566},
  year      = {2010},
  abstract  = {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.},
  language  = {en}
}
@unpublished{FradonRoelly2009,
  author    = {Fradon, Myriam and Roelly, Sylvie},
  title     = {Infinitely many Brownian globules with Brownian radii},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49552},
  year      = {2009},
  abstract  = {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.},
  language  = {en}
}
@unpublished{Penisson2009,
  author    = {P{\´e}nisson, Sophie},
  title     = {Continuous-time multitype branching processes conditioned on very late extinction},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49548},
  year      = {2009},
  abstract  = {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.},
  language  = {en}
}
@unpublished{Rafler2009,
  author    = {Rafler, Mathias},
  title     = {Gaussian loop- and polya processes : a point process approach},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51638},
  year      = {2009},
  abstract  = {Zuf{\"a}llige Punktprozesse beschreiben eine (zuf{\"a}llige) zeitliche Abfolge von Ereignissen oder eine (zuf{\"a}llige) r{\"a}umliche Anordnung von Objekten. Deren wichtigster Vertreter ist der Poissonprozess. Der Poissonprozess zum Intensit{\"a}tsmaß, das Lebesgue-Maß ordnet jedem Gebiet sein Volumen zu, erzeugt lokal, d.h in einem beschr{\"a}nkten Gebiet B, gerade eine mit dem Volumen von B poissonverteilte Anzahl von Punkten, die identisch und unabh{\"a}ngig 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 gen{\"u}gend Informationen, um Statistik betreiben zu k{\"o}nnen: Bedingt man lokal bzgl. der Anzahl der Teilchen einer Stichprobe, so fragt man nach allen Punktprozessen, die eine solche Beobachtung h{\"a}tten liefern k{\"o}nnen. Diese sind Limespunktprozesse zu dieser Beobachtung. Kommt mehr als einer in Frage, spricht man von einem Phasen{\"u}bergang. Da die Menge dieser Limespunktprozesse konvex ist, fragt man nach deren Extremalpunkten, dem Rand. Im ersten Teil wird ein Poissonprozess f{\"u}r ein physikalisches Teilchenmodell f{\"u}r Bosonen konstruiert. Dieses erzeugt sogenannte Loops, das sind geschlossene Polygonz{\"u}ge, die dadurch charakterisiert sind, dass man an einem Ort mit einem Punkt startet, den mit einem normalverteilten Schritt l{\"a}uft und dabei nach einer gegebenen, aber zuf{\"a}lligen Anzahl von Schritten zum Ausgangspunkt zur{\"u}ckkehrt. F{\"u}r verschiedene Beobachtungen von Stichproben werden zugeh{\"o}rige Limespunktprozesse diskutiert. Diese Beobachtungen umfassen etwa das Z{\"a}hlen der Loops gem{\"a}aß ihrer L{\"a}nge, das Z{\"a}hlen der Loops insgesamt, oder das Z{\"a}hlen der von den Loops gemachten Schritte. Jede Wahl zieht eine charakteristische Struktur der invarianten Punktprozesse nach sich. In allen hiesigen F{\"a}llen wird ein charakteristischer Phasen{\"u}bergang gezeigt und Extremalpunkte werden als spezielle Poissonprozesse identifiziert. Insbesondere wird gezeigt, wie die Wahl der Beobachtung die L{\"a}nge 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 L{\"a}nge 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 unabh{\"a}ngig 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 "T{\"u}rmchen", indem sich verschiedene Punkte am selben Ort stapeln. Es wird gezeigt, dass dennoch grundlegende Eigenschaften mit denjenigen des Poissonprozesses {\"u}bereinstimmen, dazu geh{\"o}ren unendliche Teilbarkeit sowie Unabh{\"a}ngigkeit der Zuw{\"a}chse. Zudem werden sein Laplace-Funktional sowie seine Palmsche Verteilung bestimmt. Letztere zeigt, dass die H{\"o}he der T{\"u}rmchen gerade geometrisch verteilt ist. Abschließend werden wiederum Statistiken, nun f{\"u}r den Summenprozess, diskutiert. Je nach Art der Beobachtung von der Stichprobe, etwa Anzahl, Gesamth{\"o}he der T{\"u}rmchen oder beides, gibt es in jedem der drei F{\"a}lle charakteristische Limespunktprozesse und es stellt sich heraus, dass die zugeh{\"o}rigen Extremalverteilungen wiederum Polyasche Summenprozesse sind.},
  language  = {en}
}
@unpublished{RedigRoellyRuszel2009,
  author    = {Redig, Frank and Roelly, Sylvie and Ruszel, Wioletta},
  title     = {Short-time Gibbsianness for infinite-dimensional diffusions with space-time interaction},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49514},
  year      = {2009},
  abstract  = {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.},
  language  = {de}
}
@unpublished{LouisRouquier2009,
  author    = {Louis, Pierre-Yves and Rouquier, Jean-Baptiste},
  title     = {Time-to-Coalescence for interacting particle systems : parallel versus sequential updating},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49454},
  year      = {2009},
  abstract  = {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.},
  language  = {en}
}
@unpublished{Keller2009,
  author    = {Keller, Peter},
  title     = {Erzeugung gleichverteilter Stichproben von Lozenge-Teilungen mittels Kopplung von Markovketten},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49506},
  year      = {2009},
  abstract  = {Aus dem Inhalt: 1 Einleitung 2 Eigenschaften der Lozengeteilungen 3 Coupling From The Past (CFTP) 4 Simulation von uniform verteilten Lozengeteilungen 5 Programmlisting und Diskussion der Implementierung 6 Ausblick A Anhang},
  language  = {de}
}
@unpublished{Anders2009,
  author    = {Anders, Martin},
  title     = {Martingale, Amarts und das starke Gesetz der Grossen Zahlen},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49494},
  year      = {2009},
  abstract  = {Aus dem Inhalt: Einleitung Kapitel 1. Starke Gesetze der Grossen Zahlen 1. SGGZ unter Wachstumsbedingungen an die p-ten Momente 2. SGGZ f{\"u}r identisch verteilte Zufallsvariablen 3. SGGZ f{\"u}r Prozesse mit *-mixing-Eigenschaft Kapitel 2. Einf{\"u}hrung zu diskreten (Sub-,Super-)Martingalen 1. Vorhersagbarkeit 2. gestoppte (Sub-,Super-)Martingale 3. Upcrossings 4. Konvergenzs{\"a}tze 5. Doob-Zerlegung 6. Eine {\"a}quivalente Definition eines (Sub-)Martingals Kapitel 3. Martingale und gleichgradige Integrierbarkeit 1. Gleichm{\"a}ßige(-f¨ormige,-gradige) Integrierbarkeit 2. gleichgradig integrierbare Martingale Kapitel 4. Martingale und das SGGZ Kapitel 5."reversed" (Sub-,Super-)Martingale 1. Konvergenzs{\"a}tze Kapitel 6. (Sub-,Super-)Martingale mit gerichteter Indexmenge 1. {\"A}quivalente Formulierung eines (Sub-)Martingals 2. Konvergenzs{\"a}tze Kapitel 7. Quasimartingale,Amarts und Semiamarts 1. Konvergenzs{\"a}tze 2. Riesz-Zerlegung 3. Doob-Zerlegung Kapitel 8. Amarts und das SGGZ Kapitel 9."reversed" Amarts und Semiamarts 1. Konvergenzs{\"a}tze 2."Aufw{\"a}rts"- gegen "Abw{\"a}rts"-Adaptiertheit 3. Riesz-Zerlegung 4. Stabilit{\"a}tsanalyse Kapitel 10. Amarts mit gerichteter Indexmenge 1. Konvergenzs{\"a}tze 2. Riesz-Zerlegung Anhang A. zur Existenz einer Folge unabh{\"a}ngiger Zufallsvariablen B. Konvergenz},
  language  = {de}
}
@unpublished{Laeuter2008,
  author    = {L{\"a}uter, Henning},
  title     = {Empirical Minimax Linear Estimates},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49483},
  year      = {2008},
  abstract  = {We give the explicit solution for the minimax linear estimate. For scale dependent models an empirical minimax linear estimates is de¯ned and we prove that these estimates are Stein's estimates.},
  language  = {en}
}
@unpublished{Murr2008,
  author    = {Murr, R{\"u}diger},
  title     = {Dualit{\"a}tsformeln f{\"u}r Brownsche Bewegung und f{\"u}r eine Irrfahrt mit Anwendung am Konvergenzergebnis von Donsker},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49476},
  year      = {2008},
  abstract  = {Aus dem Inhalt: 0.1 Danksagung 0.2 Einleitung 1 Allgemeines und Grundlagen 1.1 Die Brownsche Bewegung 2 Die Dualit{\"a}tsformel des Wienermaßes 2.1 Wienermaß erf{\"u}llt Dualit{\"a}tsformel 2.2 Dualit{\"a}tsformel charakterisiert Wienermaß 3 Die diskrete Dualit{\"a}tsformel der Irrfahrt 3.1 Verallgemeinerte symmetrische Irrfahrt erf{\"u}llt diskrete Dualit{\"a}tsformel 3.2 Diskrete Dualit{\"a}tsformel charakterisiert verallgemeinerte symmetrische Irrfahrt 4 Donskers Theorem und die Dualit{\"a}tsformeln 4.1 Straffheit der renormierten stetigen Irrfahrt 4.2 Konvergenz der Irrfahrt 5 Anhang},
  language  = {de}
}
@unpublished{Zehmisch2008,
  author    = {Zehmisch, Ren{\´e}},
  title     = {{\"U}ber Waldidentit{\"a}ten der Brownschen Bewegung},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49469},
  year      = {2008},
  abstract  = {Aus dem Inhalt: 1 Abraham Wald (1902-1950) 2 Einf{\"u}hrung der Grundbegriffe. Einige technische bekannte Ergebnisse 2.1 Martingal und Doob-Ungleichung 2.2 Brownsche Bewegung und spezielle Martingale 2.3 Gleichgradige Integrierbarkeit von Prozessen 2.4 Gestopptes Martingal 2.5 Optionaler Stoppsatz von Doob 2.6 Lokales Martingal 2.7 Quadratische Variation 2.8 Die Dichte der ersten einseitigen {\"U}berschreitungszeit der Brown- schen Bewegung 2.9 Waldidentit{\"a}ten f{\"u}r die {\"U}berschreitungszeiten der Brownschen Bewegung 3 Erste Waldidentit{\"a}t 3.1 Burkholder, Gundy und Davis Ungleichungen der gestoppten Brown- schen Bewegung 3.2 Erste Waldidentit{\"a}t f{\"u}r die Brownsche Bewegung 3.3 Verfeinerungen der ersten Waldidentit{\"a}t 3.4 St{\"a}rkere Verfeinerung der ersten Waldidentit{\"a}t f{\"u}r die Brown- schen Bewegung 3.5 Verfeinerung der ersten Waldidentit{\"a}t f{\"u}r spezielle Stoppzeiten der Brownschen Bewegung 3.6 Beispiele f{\"u}r lokale Martingale f{\"u}r die Verfeinerung der ersten Waldidentit{\"a}t 3.7 {\"U}berschreitungszeiten der Brownschen Bewegung f{\"u}r nichtlineare Schranken 4 Zweite Waldidentit{\"a}t 4.1 Zweite Waldidentit{\"a}t f{\"u}r die Brownsche Bewegung 4.2 Anwendungen der ersten und zweitenWaldidentit{\"a}t f{\"u}r die Brown- schen Bewegung 5 Dritte Waldidentit{\"a}t 5.1 Dritte Waldidentit{\"a}t f{\"u}r die Brownsche Bewegung 5.2 Verfeinerung der dritten Waldidentit{\"a}t 5.3 Eine wichtige Voraussetzung f{\"u}r die Verfeinerung der drittenWal- didentit{\"a}t 5.4 Verfeinerung der dritten Waldidentit{\"a}t f{\"u}r spezielle Stoppzeiten der Brownschen Bewegung 6 Waldidentit{\"a}ten im Mehrdimensionalen 6.1 Erste Waldidentit{\"a}t im Mehrdimensionalen 6.2 Zweite Waldidentit{\"a}t im Mehrdimensionalen 6.3 Dritte Waldidentit{\"a}t im Mehrdimensionalen 7 Appendix},
  language  = {de}
}
@unpublished{Rafler2008,
  author    = {Rafler, Mathias},
  title     = {Martin-Dynkin Boundaries of the Bose Gas},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51667},
  year      = {2008},
  abstract  = {The Ginibre gas is a Poisson point process defined on a space of loops related to the Feynman-Kac representation of the ideal Bose gas. Here we study thermodynamic limits of different ensembles via Martin-Dynkin boundary technique and show, in which way infinitely long loops occur. This effect is the so-called Bose-Einstein condensation.},
  language  = {en}
}
@unpublished{KleinZitt2008,
  author    = {Klein, Markus and Zitt, Pierre-Andr{\´e}},
  title     = {Resonances for a diffusion with small noise},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49448},
  year      = {2008},
  abstract  = {We study resonances for the generator of a diffusion with small noise in R(d) : L = -∈∆ + ∇F * ∇, when the potential F grows slowly at infinity (typically as a square root of the norm). The case when F grows fast is well known, and under suitable conditions one can show that there exists a family of exponentially small eigenvalues, related to the wells of F. We show that, for an F with a slow growth, the spectrum is R+, but we can find a family of resonances whose real parts behave as the eigenvalues of the "quick growth" case, and whose imaginary parts are small.},
  language  = {en}
}
@unpublished{PraLouisMinelli2008,
  author    = {Pra, Paolo Dai and Louis, Pierre-Yves and Minelli, Ida G.},
  title     = {Complete monotone coupling for Markov processes},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-18286},
  year      = {2008},
  abstract  = {We formalize and analyze the notions of monotonicity and complete monotonicity for Markov Chains in continuous-time, taking values in a finite partially ordered set. Similarly to what happens in discrete-time, the two notions are not equivalent. However, we show that there are partially ordered sets for which monotonicity and complete monotonicity coincide in continuoustime but not in discrete-time.},
  language  = {de}
}
@unpublished{CattiauxDaiPraPoelly2007,
  author    = {Cattiaux, Patrick and Dai Pra, Paolo and Poelly, Sylvie},
  title     = {A constructive approach to a class of ergodic HJB equations with nonsmooth cost},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49430},
  year      = {2007},
  abstract  = {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.},
  language  = {en}
}
@unpublished{ChampagnatRoelly2007,
  author    = {Champagnat, Nicolas and Roelly, Sylvie},
  title     = {Limit theorems for conditioned multitype Dawson-Watanabe processes},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49426},
  year      = {2007},
  abstract  = {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.},
  language  = {en}
}
@unpublished{Laeuter2006,
  author    = {L{\"a}uter, Henning},
  title     = {On approximate likelihood in survival models},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51615},
  year      = {2006},
  abstract  = {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.},
  language  = {en}
}
@unpublished{LieroLiero2006,
  author    = {Liero, Hannelore and Liero, Matthias},
  title     = {Testing the acceleration function in life time models},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49405},
  year      = {2006},
  abstract  = {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.},
  language  = {en}
}
@unpublished{Liero2006,
  author    = {Liero, Hannelore},
  title     = {A Note on : testing the Copula Based on Densities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49393},
  year      = {2006},
  abstract  = {We consider the problem of testing whether the density of a mul- tivariate random variable can be expressed by a prespecified copula function and the marginal densities. The proposed test procedure is based on the asymptotic normality of the properly standardized integrated squared distance between a multivariate kernel density estimator and an estimator of its expectation under the hypothesis. The test of independence is a special case of this approach.},
  language  = {en}
}
@unpublished{FradonRoelly2005,
  author    = {Fradon, Myriam and Roelly, Sylvie},
  title     = {Brownian Hard Balls submitted to an infinite rangeinteraction with slow decay},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49379},
  year      = {2005},
  abstract  = {We consider an infinite system of hard balls in Rd undergoing Brownian motions and submitted to a pair potential with infinite range and quasi polynomial decay. It is modelized by an infinite-dimensional Stochastic Differential Equation with an infinite-dimensional local time term. Existence and uniqueness of a strong solution is proven for such an equation with deterministic initial condition. We also show that the set of all equilibrium measures, solution of a Detailed Balance Equation, coincides with the set of canonical Gibbs measures associated to the hard core potential.},
  language  = {en}
}
@unpublished{FradonRoelly2005,
  author    = {Fradon, Myriam and Roelly, Sylvie},
  title     = {Infinite system of Brownian Balls: Equilibrium measures are canonical Gibbs},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51594},
  year      = {2005},
  abstract  = {We consider a system of infinitely many hard balls in Rd undergoing Brownian motions and submitted to a smooth pair potential. It is modelized by an infinite-dimensional Stochastic Differential Equation with a local time term. We prove that the set of all equilibrium measures, solution of a Detailed Balance Equation, coincides with the set of canonical Gibbs measures associated to the hard core potential added to the smooth interaction potential.},
  language  = {en}
}
@unpublished{FradonRoelly2005,
  author    = {Fradon, Myriam and Roelly, Sylvie},
  title     = {Infinite system of Brownian balls with interaction : the non-reversible case},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51546},
  year      = {2005},
  abstract  = {We consider an infinite system of hard balls in Rd undergoing Brownian motions and submitted to a smooth pair potential. It is modelized by an infinite- dimensional Stochastic Differential Equation with an infinite-dimensional local time term. Existence and uniqueness of a strong solution is proven for such an equation with fixed deterministic initial condition. We also show that Gibbs measures are reversible measures.},
  language  = {en}
}
@unpublished{DereudreRoelly2004,
  author    = {Dereudre, David and Roelly, Sylvie},
  title     = {Propagation of Gibbsianness for infinite-dimensional gradient Brownian diffusions},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51535},
  year      = {2004},
  abstract  = {We study the (strong-)Gibbsian character on RZd of the law at time t of an infinitedimensional gradient Brownian diffusion , when the initial distribution is Gibbsian.},
  language  = {en}
}
@unpublished{LaeuterLiero2004,
  author    = {L{\"a}uter, Henning and Liero, Hannelore},
  title     = {Nonparametric estimation and testing in survival models},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51586},
  year      = {2004},
  abstract  = {The aim of this paper is to demonstrate that nonparametric smoothing methods for estimating functions can be an useful tool in the analysis of life time data. After stating some basic notations we will present a data example. Applying standard parametric methods to these data we will see that this approach fails - basic features of the underlying functions are not reflected by their estimates. Our proposal is to use nonparametric estimation methods. These methods are explained in section 2. Nonparametric approaches are better in the sense that they are more flexible, and misspecifications of the model are avoided. But, parametric models have the advantage that the parameters can be interpreted. So, finally, we will formulate a test procedure to check whether a parametric or a nonparametric model is appropriate.},
  language  = {en}
}
@unpublished{Louis2004,
  author    = {Louis, Pierre-Yves},
  title     = {Increasing Coupling of Probabilistic Cellular Automata},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51578},
  year      = {2004},
  abstract  = {We give a necessary and sufficient condition for the existence of an increasing coupling of N (N >= 2) synchronous dynamics on S-Zd (PCA). Increasing means the coupling preserves stochastic ordering. We first present our main construction theorem in the case where S is totally ordered; applications to attractive PCAs are given. When S is only partially ordered, we show on two examples that a coupling of more than two synchronous dynamics may not exist. We also prove an extension of our main result for a particular class of partially ordered spaces.},
  language  = {en}
}
@unpublished{BagdonavičiusLevulieneNikulinetal.2004,
  author    = {Bagdonavičius, Vilijandas B. and Levuliene, Ruta and Nikulin, Mikhail S. and Zdorova-Cheminade, Olga},
  title     = {Tests for homogeneity of survival distributions against non-location alternatives and analysis of the gastric cancer data},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51527},
  year      = {2004},
  abstract  = {The two and k-sample tests of equality of the survival distributions against the alternatives including cross-effects of survival functions, proportional and monotone hazard ratios, are given for the right censored data. The asymptotic power against approaching alternatives is investigated. The tests are applied to the well known chemio and radio therapy data of the Gastrointestinal Tumor Study Group. The P-values for both proposed tests are much smaller then in the case of other known tests. Differently from the test of Stablein and Koutrouvelis the new tests can be applied not only for singly but also to randomly censored data.},
  language  = {en}
}
@unpublished{Louis2004,
  author    = {Louis, Pierre-Yves},
  title     = {Coupling, space and time Mixing for parallel stochastic dynamics},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51560},
  year      = {2004},
  abstract  = {We first introduce some coupling of a finite number of Probabilistic Cellular Automata dynamics (PCA), preserving the stochastic ordering. Using this tool, for a general attractive probabilistic cellular automata on SZd, where S is finite, we prove that a condition (A) is equivalent to the (time-) convergence towards equilibrium of this Markovian parallel dynamics, in the uniform norm, exponentially fast. This condition (A) means the exponential decay of the influence from the boundary for the invariant measures of the system restricted to finite 'box'-volume. For a class of reversible PCA dynamics on {-1, +1}Zd , with a naturally associated Gibbsian potential ϕ, we prove that a Weak Mixing condition for ϕ implies the validity of the assumption (A); thus the 'exponential ergodicity' of the dynamics towards the unique Gibbs measure associated to ϕ holds. On some particular examples of this PCA class, we verify that our assumption (A) is weaker than the Dobrushin-Vasershtein ergodicity condition. For some special PCA, the 'exponential ergodicity' holds as soon as there is no phase transition.},
  language  = {en}
}
@book{DereudreRoelly2004,
  author    = {Dereudre, David and Roelly, Sylvie},
  title     = {On Gibbsianness of infinite-dimensional diffusions},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-52630},
  publisher      = {Universit{\"a}t Potsdam},
  year      = {2004},
  abstract  = {We analyse different Gibbsian properties of interactive Brownian diffusions X indexed by the lattice \$Z^{d} : X = (X_{i}(t), i ∈ Z^{d}, t ∈ [0, T], 0 < T < +∞)\$. In a first part, these processes are characterized as Gibbs states on path spaces of the form \$C([0, T],R)Z^{d}\$. In a second part, we study the Gibbsian character on \$R^{Z}^{d}\$ of \$v^{t}\$, the law at time t of the infinite-dimensional diffusion X(t), when the initial law \$v = v^{0}\$ is Gibbsian.},
  language  = {en}
}
@unpublished{Liero2003,
  author    = {Liero, Hannelore},
  title     = {Testing the Hazard Rate, Part I},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51510},
  year      = {2003},
  abstract  = {We consider a nonparametric survival model with random censoring. To test whether the hazard rate has a parametric form the unknown hazard rate is estimated by a kernel estimator. Based on a limit theorem stating the asymptotic normality of the quadratic distance of this estimator from the smoothed hypothesis an asymptotic ®-test is proposed. Since the test statistic depends on the maximum likelihood estimator for the unknown parameter in the hypothetical model properties of this parameter estimator are investigated. Power considerations complete the approach.},
  language  = {en}
}
@unpublished{Laeuter2003,
  author    = {L{\"a}uter, Henning},
  title     = {Estimation in partly parametric additive Cox models},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51509},
  year      = {2003},
  abstract  = {The dependence between survival times and covariates is described e.g. by proportional hazard models. We consider partly parametric Cox models and discuss here the estimation of interesting parameters. We represent the ma- ximum likelihood approach and extend the results of Huang (1999) from linear to nonlinear parameters. Then we investigate the least squares esti- mation and formulate conditions for the a.s. boundedness and consistency of these estimators.},
  language  = {en}
}
@unpublished{Liero2003,
  author    = {Liero, Hannelore},
  title     = {Goodness of Fit Tests of L2-Type},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51494},
  year      = {2003},
  abstract  = {We give a survey on procedures for testing functions which are based on quadratic deviation measures. The following problems are considered: Testing whether a density function lies in a parametric class of functions, whether continuous random variables are independent; testing cell probabilities and independence in sparse data sets; testing the parametric fit of a regression homoscedasticity in a regression model and testing the hazard rate in survival models with censoring and with and without covariates.},
  language  = {en}
}