FIRST EXIT TIMES OF SOLUTIONS OF STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY MULTIPLICATIVE LÉVY NOISE WITH HEAVY TAILS

Abstract

In this paper, we study first exit times from a bounded domain of a gradient dynamical system Ẏt= -∇U(Yt) perturbed by a small multiplicative Lévy noise with heavy tails. A special attention is paid to the way the multiplicative noise is introduced. In particular, we determine the asymptotics of the first exit time of solutions of Itô, Stratonovich and Marcus canonical SDEs.