Recursive computation of the invariant measure of a stochastic differential equation driven by a L\'evy process

Abstract

We investigate some recursive procedures based on an exact or ``approximate'' Euler scheme with decreasing step in vue to computation of invariant measures of solutions to S.D.E. driven by a L\'evy process. Our results are valid for a large class of S.D.E. that can be governed by L\'evy processes with few moments or can have a weakly mean-reverting drift, and permit to find again the a.s. C.L.T for stable processes.