Non uniqueness of stationary measures for self-stabilizing processes

Details Non uniqueness of stationary measures for self-stabilizing processes Non uniqueness of stationary measures for self-stabilizing processes

2009-03-13

arxiv.org/abs/0903.2460v1

Mathematics

Probability

Scientific paper

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 to point out singular phenomenons 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.

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