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