Self-interacting diffusions IV: Rate of convergence

Details Self-interacting diffusions IV: Rate of convergence Self-interacting diffusions IV: Rate of convergence

2009-07-31

arxiv.org/abs/0907.5468v1

Mathematics

Probability

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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 Bena\"im, Ledoux, Raimond (2002) and Bena\"im, 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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