Approximation of the invariant distribution for a class of ergodic jump diffusions

Gloter, A.; Honoré, I.; Loukianova, D.

ESAIM: Probability and Statistics, Tome 24 (2020), pp. 883-913.

Suite au passage du modèle économique de la revue en S20, le texte intégral des articles des années 2019 et 2020 est accessible uniquement sur le site de l'éditeur et est réservé aux abonnés.

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. This scheme is similar to those introduced in Lamberton and Pagès Bernoulli 8 (2002) 367-405. for a Brownian diffusion and extended in F. Panloup, Ann. Appl. Probab. 18 (2008) 379-426. to a diffusion with Lévy jumps. We obtain a non-asymptotic quasi Gaussian (asymptotically Gaussian) concentration bound for the difference between the invariant distribution and the empirical distribution computed with the scheme of decreasing time step along appropriate test functions f such that f − ν(f) is a coboundary of the infinitesimal generator.

Classification : 60H35, 60G51, 60E15, 65C30
Mots-clés : Invariant distribution, diffusion processes, jump processes, inhomogeneous Markov chains, non-asymptotic Gaussian concentration

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