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

Julian Tugaut

Stochastic Processes and their Applications, 2013, vol. 123, issue 5, 1780-1801

Abstract: 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 {μt;t≥0}, μt being the law of the diffusion. Moreover, we establish the weak convergence under an additional hypothesis.

Keywords: Self-interacting diffusion; Free-energy; McKean–Vlasov stochastic differential equations; Multi-wells potential; Granular media equation (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:123:y:2013:i:5:p:1780-1801

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DOI: 10.1016/j.spa.2012.12.003

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