Non-uniqueness of stationary measures for self-stabilizing processes

S. Herrmann and J. Tugaut

Stochastic Processes and their Applications, 2010, vol. 120, issue 7, 1215-1246

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: Self-interacting; diffusion; Stationary; measures; Double-well; potential; Perturbed; dynamical; system; Laplace's; method; Fixed; point; theorem; McKean-Vlasov; stochastic; differential; equations (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (3)

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