Convergence rates for annealing diffusion processes

Abstract

We consider the annealing diffusion process and investigate convergence rates. Namely, for the diffusion dXt = -∇V(Xt) dt + σ(t) dBt, where (Bt)t ≤ 0 is the d-dimensional Brownian motion and σ(t) decreases to zero, we prove a large deviation principle for (V(Xt)) and weak convergence of (σ-2(t)(V(Xt) - inf V)).