TY - GEN A1 - Roelly, Sylvie A1 - Sortais, Michel T1 - Space-time asymptotics of an infinite-dimensional diffusion having a long- range memory N2 - We develop a cluster expansion in space-time for an infinite-dimensional system of interacting diffusions where the drift term of each diffusion depends on the whole past of the trajectory; these interacting diffusions arise when considering the Langevin dynamics of a ferromagnetic system submitted to a disordered external magnetic field. KW - Random Field Ising Model KW - Langevin Dynamics KW - Interacting Diffusion Processes KW - Space-Time Cluster Expansions Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-6700 ER - TY - GEN A1 - Roelly, Sylvie A1 - Thieullen, Michèle T1 - Duality formula for the bridges of a Brownian diffusion : application to gradient drifts N2 - In this paper, we consider families of time Markov fields (or reciprocal classes) which have the same bridges as a Brownian diffusion. We characterize each class as the set of solutions of an integration by parts formula on the space of continuous paths C[0; 1]; R-d) Our techniques provide a characterization of gradient diffusions by a duality formula and, in case of reversibility, a generalization of a result of Kolmogorov. KW - reciprocal processes KW - stochastic bridge KW - mixture of bridges KW - integration by parts formula KW - Malliavin calculus KW - entropy KW - time reversal Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-6710 ER - TY - GEN A1 - Louis, Pierre-Yves T1 - Ergodicity of PCA BT - equivalence between spatial and temporal mixing conditions N2 - For a general attractive Probabilistic Cellular Automata on S-Zd, we prove that the (time-) convergence towards equilibrium of this Markovian parallel dynamics, exponentially fast in the uniform norm, is equivalent to a condition (A). This condition means the exponential decay of the influence from the boundary for the invariant measures of the system restricted to finite boxes. For a class of reversible PCA dynamics on {1,+1}(Zd), wit a naturally associated Gibbsian potential rho, we prove that a (spatial-) weak mixing condition (WM) for rho implies the validity of the assumption (A); thus exponential (time-) ergodicity of these dynamics towards the unique Gibbs measure associated to rho hods. On some particular examples we state that exponential ergodicity holds as soon as there is no phase transition. KW - Wahrscheinlichkeitstheorie KW - Wechselwirkende Teilchensysteme KW - Stochastische Zellulare Automaten KW - Interacting particle systems KW - Probabilistic Cellular Automata KW - ERgodicity of Markov Chains KW - Gibbs measures Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-6589 ER - TY - GEN A1 - Louis, Pierre-Yves T1 - Increasing coupling for probabilistic cellular automata N2 - 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. KW - Wahrscheinlichkeitstheorie KW - stochastische Anordnung KW - stochastische Zellulare Automaten KW - Kopplung KW - stochastic ordering KW - Probabilistic Cellular Automata KW - monotone coupling Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-6593 ER - TY - GEN A1 - Roelly, Sylvie A1 - Dai Pra, Paolo T1 - An existence result for infinite-dimensional Brownian diffusions with non- regular and non Markovian drift N2 - We prove in this paper an existence result for infinite-dimensional stationary interactive Brownian diffusions. The interaction is supposed to be small in the norm ||.||∞ but otherwise is very general, being possibly non-regular and non-Markovian. Our method consists in using the characterization of such diffusions as space-time Gibbs fields so that we construct them by space-time cluster expansions in the small coupling parameter. KW - infinite-dimensional Brownian diffusion KW - space-time Gibbs field KW - cluster expansion Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-6684 ER - TY - GEN A1 - Pornsawad, Pornsarp A1 - Sungcharoen, Parada A1 - Böckmann, Christine T1 - Convergence rate of the modified Landweber method for solving inverse potential problems T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - In this paper, we present the convergence rate analysis of the modified Landweber method under logarithmic source condition for nonlinear ill-posed problems. The regularization parameter is chosen according to the discrepancy principle. The reconstructions of the shape of an unknown domain for an inverse potential problem by using the modified Landweber method are exhibited. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1034 KW - nonlinear operator KW - regularization KW - modified Landweber method KW - discrepancy principle KW - logarithmic source condition Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-471942 SN - 1866-8372 IS - 1034 ER - TY - GEN A1 - Reich, Sebastian T1 - On a geometrical interpretation of differential-algebraic equations N2 - The subject of this paper is the relation of differential-algebraic equations (DAEs) to vector fields on manifolds. For that reason, we introduce the notion of a regular DAE as a DAE to which a vector field uniquely corresponds. Furthermore, a technique is described which yields a family of manifolds for a given DAE. This socalled family of constraint manifolds allows in turn the formulation of sufficient conditions for the regularity of a DAE. and the definition of the index of a regular DAE. We also state a method for the reduction of higher-index DAEs to lowsr-index ones that can be solved without introducing additional constants of integration. Finally, the notion of realizability of a given vector field by a regular DAE is introduced, and it is shown that any vector field can be realized by a regular DAE. Throughout this paper the problem of path-tracing is discussed as an illustration of the mathematical phenomena. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 157 Y1 - 1990 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-46683 ER - TY - GEN A1 - Champagnat, Nicolas A1 - Roelly, Sylvie T1 - Limit theorems for conditioned multitype Dawson-Watanabe processes and Feller diffusions N2 - A multitype Dawson-Watanabe process is conditioned, in subcritical and critical cases, on non-extinction in the remote future. On every finite time interval, its distribution is absolutely continuous with respect to the law of the unconditioned process. A martingale problem characterization is also given. Several results on the long time behavior of the conditioned mass process - the conditioned multitype Feller branching diffusion - are then proved. The general case is first considered, where the mutation matrix which models the interaction between the types, is irreducible. Several two-type models with decomposable mutation matrices are analyzed too . T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 065 KW - multitype measure-valued branching processes KW - conditioned KW - critical and subcritical Dawson-Watanabe process KW - conditioned Feller diffusion Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-18610 ER - TY - GEN A1 - Reich, Sebastian T1 - Momentum conserving symplectic integrators N2 - In this paper, we show that symplectic partitioned Runge-Kutta methods conserve momentum maps corresponding to linear symmetry groups acting on the phase space of Hamiltonian differential equations by extended point transformation. We also generalize this result to constrained systems and show how this conservation property relates to the symplectic integration of Lie-Poisson systems on certain submanifolds of the general matrix group GL(n). T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 044 Y1 - 1994 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-16824 ER - TY - GEN A1 - Imkeller, Peter A1 - Roelly, Sylvie T1 - Die Wiederentdeckung eines Mathematikers: Wolfgang Döblin N2 - "Considerons une particule mobile se mouvant aleatoirement sur la droite (ou sur un segment de droite). Supposons qu'il existe une probabilite F(x,y;s,t) bien definie pour que la particule se trouvant a l'instant s dans la position x se trouve a l'instant t (> s) a gauche de y, probabilite independante du mouvement anterieur de la particule...." Mit diesen Worten beginnt eines der berühmtesten mathematischen Manuskripte des letzten Jahrhunderts. Es stammt vom Soldaten Wolfgang Döblin, Sohn des deutschen Schriftstellers Alfred Döblin, und trägt den Titel "Sur l'equation de Kolmogoroff". Seine Veröffentlichung verbindet sich mit einer unglaublichen Geschichte. Wolfgang Döblin, stationiert mit seiner Einheit in den Ardennen im Winter 1939/1940, arbeitete an diesem Manuskript. Er entschloss sich, es als versiegeltes Manuskript an die Academie des Sciences in Paris zu schicken. Aber er kehrte nie aus diesem Krieg zurück. Sein Manuskript blieb 60 Jahre unter Verschluss im Archiv, und wurde erst im Jahre 2000 geöffnet. Wie weit Döblin damit seiner Zeit voraus war, wurde erkannt, nachdem es von Bernard Bru und Marc Yor ausgewertet worden war. Im ersten Satz umschreibt W. Döblin gleichzeitig das Programm des Manuskripts: "Wir betrachten ein bewegliches Teilchen, das sich zufällig auf der Geraden (oder einem Teil davon) bewegt." Er widmet sich damit der Aufgabe, die Fundamente eines Gebiets zu legen, das wir heute als stochastische Analysis bezeichnen. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 035 KW - Kolmogorov-Gleichung KW - Stochastische Analysis KW - Döblin KW - Wolfgang KW - Doblin KW - Vincent KW - Doeblin KW - Wolfgang Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-16397 ER -