A Kramers' type law for self-interacting diffusions

We study the exit time of a domain for a self-interacting diffusion, where the Brownian motion is replaced by σBt for a constant σ. We first show that the rate of convergence previously obtained for a convex confinment potential V and a convex interaction potential does not depend on σ. Then, we show a Kramers' type law for the first exit-time from a domain (satisfying classical hypotheses)