NON-ASYMPTOTIC CONCENTRATION INEQUALITY FOR AN APPROXIMATION OF THE INVARIANT DISTRIBUTION OF A DIFFUSION DRIVEN BY COMPOUND POISSON PROCESS

In this article we approximate the invariant distribution ν of an ergodic Jump Diffusion driven by the sum of a Brownian motion and a Compound Poisson process with sub-Gaussian jumps. We first construct an Euler discretization scheme with decreasing time steps, particularly suitable in cases where the driving Levy process is a Compound Poisson. This scheme is similar to those introduced by Lamberton and Pages in [LP02] for a Brownian diffusion and extended by Panloup in [Pan08b] to the Jump Diffusion with Levy jumps. We obtain a non-asymptotic Gaussian concentration bound for the difference between the invariant distribution and the empirical distribution computed with the scheme of decreasing time step along a appropriate test functions f such that f − ν(f) is is a coboundary of the infinitesimal generator.