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Non-uniqueness of stationary measures for self-stabilizing processes
Authors:S Herrmann  J Tugaut
Institution:Institut de Mathématiques Elie Cartan - UMR 7502, Nancy-Université, CNRS, INRIA, B.P. 239, 54506 Vandoeuvre-lès-Nancy Cedex, France
Abstract: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.
Keywords:primary  60H10  secondary  60J60  60G10  41A60
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