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2011 Self-Interacting Diffusions IV: Rate of Convergence
Michel Benaïm, Olivier Raimond
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Electron. J. Probab. 16: 1815-1843 (2011). DOI: 10.1214/EJP.v16-948

Abstract

Self-interacting diffusions are processes living on a compact Riemannian manifold defined by a stochastic differential equation with a drift term depending on the past empirical measure of the process. The asymptotics of this measure is governed by a deterministic dynamical system and under certain conditions it converges almost surely towards a deterministic measure. (see Benaïm, Ledoux, Raimond (2002) and Benaïm, Raimond (2005)). We are interested here in the rate of this convergence. A central limit theorem is proved. In particular, this shows that greater is the interaction repelling faster is the convergence.

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Michel Benaïm. Olivier Raimond. "Self-Interacting Diffusions IV: Rate of Convergence." Electron. J. Probab. 16 1815 - 1843, 2011. https://doi.org/10.1214/EJP.v16-948

Information

Accepted: 14 October 2011; Published: 2011
First available in Project Euclid: 1 June 2016

zbMATH: 1245.60089
MathSciNet: MR2842088
Digital Object Identifier: 10.1214/EJP.v16-948

Subjects:
Primary: 60K35

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