Limite ergodique de processus de diffusion infini-dimensionnels

We give a temporal ergodicity criterium for the solution of a class of infinite dimensional stochastic differential equations of gradient type, where the interaction has infinite range. We illustrate our theoretical result by typical examples

Invariance principle for martingale-difference random fields

A convergence criterium to the multi-parameter Wiener process is proved. Then, it is used to establish that a martingale-difference random field on the lattice satisfies an invariance principle.Central limit theorem Multi-parameter Wiener process Martingale-difference random field Invariance principle

Limite ergodique de processus de diffusion infini-dimensionnels

We give a temporal ergodicity criterium for the solution of a class of infinite dimensional stochastic differential equations of gradient type, where the interaction has infinite range. We illustrate our theoretical result by typical examples

An existence result for infinite-dimensional Brownian diffusions with non-regular and non-Markovian drift

We prove in this paper an existence result for in nite-dimensional stationary weakly interactive Brownian diusions. The interaction is very general in the sense that it is not supposed to be regular, and it also could be non-Markovian, but it is small enough. Our method consists in using the characterization of such diusions as space-time Gibbs elds so that we construct them by space-time cluster expansions in the small coupling parameter

An existence result for infinite-dimensional Brownian diffusions with non-regular and non-Markovian drift

none2We prove in this paper an existence result for in nite-dimensional stationary weakly interactive Brownian diusions. The interaction is very general in the sense that it is not supposed to be regular, and it also could be non-Markovian, but it is small enough. Our method consists in using the characterization of such diusions as space-time Gibbs elds so that we construct them by space-time cluster expansions in the small coupling parameter.noneDAI PRA P.; ROELLY S.DAI PRA, Paolo; Roelly, S

Stochastic dynamics for an infinite system of random closed strings: A Gibbsian point of view

AbstractWe consider the stochastic dynamics of infinitely many, interacting random closed strings, and show that the law of this process can be characterized as a Gibbs state for some Hamiltonian on the path level, which is represented in terms of the interaction. This is done by means of the stochastic calculus of variations, in particular an integration by parts formula in infinite dimensions.This Gibbsian point of view of the stochastic dynamics allows us to characterize the reversible states as the Gibbs states for the underlying interaction. Under supplementary monotonicity conditions, there is only one stationary distribution, and we prove that there is exactly one Gibbs state

Phase separation and sharp large deviations

Using a refined analysis of phase boundaries, we derive sharp asymptotics of the large deviation probabilities for the total magnetisation of a low-temperature Ising model in two dimensions

Stochastic dynamics for an infinite system of random closed strings: A Gibbsian point of view

We consider the stochastic dynamics of infinitely many, interacting random closed strings, and show that the law of this process can be characterized as a Gibbs state for some Hamiltonian on the path level, which is represented in terms of the interaction. This is done by means of the stochastic calculus of variations, in particular an integration by parts formula in infinite dimensions. This Gibbsian point of view of the stochastic dynamics allows us to characterize the reversible states as the Gibbs states for the underlying interaction. Under supplementary monotonicity conditions, there is only one stationary distribution, and we prove that there is exactly one Gibbs state.Stochastic dynamics Interacting strings Stochastic quantization Gibbsian measure Integration by parts formula Reversible state

Sur la mecanique statistique d'une particule Brownienne sur le tore

SIGLETIB: RO 5073(442) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman