Self-stabilizing processes in multi-wells landscape in Rd-convergence

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:123

Article

Tugaut, Julian

关键词: Self-interacting diffusion;    Free-energy;    McKean-Vlasov stochastic differential equations;    Multi-wells potential;    Granular media equation;   

DOI  :  10.1016/j.spa.2012.12.003

来源: Elsevier

【 摘 要 】

Self-stabilizing processes are inhomogeneous diffusions in which the law of the process intervenes in the drift. If the external force is the gradient of a convex potential, it has been proved that the process converges towards the unique invariant probability as the time goes to infinity. However, in a previous article, we established that the diffusion may admit several invariant probabilities, provided that the external force derives from a non-convex potential. We here provide results about the limiting values of the family {mu(t); t >= 0}, mu(t) being the law of the diffusion. Moreover, we establish the weak convergence under an additional hypothesis. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free