Self-interacting diffusions IV: Rate of convergence

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 mu(t) of the process. The asymptotics of mu(t) is governed by a deterministic dynamical system and under certain conditions (mu(t)) converges almost surely towards a deterministic measure mu* (see Bena m, Ledoux, Raimond (2002) and Bena m, Raimond (2005)). We are interested here in the rate of convergence of mu(t) towards mu*. A central limit theorem is proved. In particular, this shows that greater is the interaction repelling faster is the convergence.