Convergence rates for annealing diffusion processes

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