Simulated annealing for Lévy-driven jump-diffusions

We consider a one-dimensional dynamical system driven by a vector field -U', where U is a multi-well potential satisfying some regularity conditions. We perturb this dynamical system by a stable symmetric non-Gaussian Lévy process whose scale decreases as a power function of time. It turns out that the limiting behaviour of the perturbed dynamical system is different for slow and fast decrease rates of the noise intensity. As opposed to the well-studied Gaussian case, the support of the limiting law is not located in the set of global minima of U.