Non-uniqueness of stationary measures for self-stabilizing processes

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:120

Article

Herrmann, S.¹  Tugaut, J.¹ 

[1] Nancy Univ, CNRS, INRIA, Inst Math Elie Cartan,UMR 7502, F-54506 Vandoeuvre Les Nancy, France

关键词: Self-interacting diffusion;    Stationary measures;    Double-well potential;    Perturbed dynamical system;    Laplace's method;    Fixed point theorem;    McKean-Vlasov stochastic differential equations;   

DOI  :  10.1016/j.spa.2010.03.009

来源: Elsevier

【 摘 要 】

We investigate the existence of invariant measures for self-stabilizing diffusions. These stochastic processes represent roughly the behavior of some Brownian particle moving in a double-well landscape and attracted by its own law. This specific self-interaction leads to nonlinear stochastic differential equations and permits pointing out singular phenomena like non-uniqueness of associated stationary measures. The existence of several invariant measures is essentially based on the non-convex environment and requires generalized Laplace's method approximations. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free