Lévy flights: transitions and meta-stability

Abstract

We consider Lévy flights of stability index α ∊ (0, 2) in a potential landscape in the limit of a small noise parameter. We give a purely probabilistic description of the random dynamics on the basis of a special decomposition of the driving Lévy processes into independent small jumps and compound Poisson parts. We prove that escape times from a potential well are exponentially distributed and their mean values increase as a power ε−α of the noise intensity ε. This allows us to obtain meta-stability results for a jump diffusion in a double-well potential.