Convergence in Distribution of Some Self-Interacting Diffusions

Aline Kurtzmann

Journal of Probability and Statistics, 2014, vol. 2014, 1-13

Abstract:

The present paper is concerned with some self-interacting diffusions living on . These diffusions are solutions to stochastic differential equations: , where is the empirical mean of the process , is an asymptotically strictly convex potential, and is a given positive function. We study the asymptotic behaviour of for three different families of functions . If with small enough, then the process converges in distribution towards the global minima of , whereas if or if , then converges in distribution if and only if .

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljps:364321

DOI: 10.1155/2014/364321

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