Lévy flights: transitions and meta-stability

Abstract

We consider Levy flights of stability index fi 2 (0,2) in a potential landscape in the limit of small noise parameter. We give a purely probabilistic description of the random dynamics based on a special decomposition of the driving Levy 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 "¡fi of the noise intensity ". This allows to obtain meta- stability results for a jump-diusion in a double-well potential.