Convergence rates for annealing diffusion processes

Abstract

We consider the annealing diffusion process and investigate convergence rates. Namely, the diffusion $dX_t = -\nabla V(X_t)dx+\sigma(t)dB_t$, where $(B_t)_t\leq 0$ is the $d$-dimensional Brownian motion and $\sigma(t)$ decreases to zero, we prove a large deviation principle for $(V(X_t))$ and weak convergence of $(\sigma^{-2}(t)(V(X_t)-\inf V)).$