Volume 24, 2020
|Page(s)||883 - 913|
|Published online||24 November 2020|
Approximation of the invariant distribution for a class of ergodic jump diffusions
Université d’Évry Val d’Essonne, Université Paris-Saclay, CNRS, Univ Evry, Laboratoire de Mathématiques et Modélisation d’Evry,
* Corresponding author: firstname.lastname@example.org
Accepted: 18 September 2020
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.
Mathematics Subject Classification: 60H35 / 60G51 / 60E15 / 65C30
Key words: Invariant distribution / diffusion processes / jump processes / inhomogeneous Markov chains / non-asymptotic Gaussian concentration
© The authors. Published by EDP Sciences, SMAI 2020
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