Exit-Problem of McKean–Vlasov Diffusions in Double-Well Landscape

Julian Tugaut ()
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Julian Tugaut: Univ Lyon, Université Jean Monnet

Journal of Theoretical Probability, 2018, vol. 31, issue 2, 1013-1023

Abstract: Abstract We consider a diffusion in which the law of the process itself appears in the drift, that is, a nonlinearity in the sense of McKean. The question that we deal with is the exit-time of such a diffusion when it evolves in a double-well landscape. This has already been solved for the convex case, but the previous methods rely completely on the convexity of the external force. Here, we provide a weak version of a Kramers’ type law for self-stabilizing process directed by a non-uniformly convex confining potential.

Keywords: Self-stabilizing diffusion; Exit-time; Large deviations; Coupling method; Granular media equation; Primary: 60F10; Secondary: 60J60; 60H10; 82C22 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10959-016-0737-x

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