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Article Dans Une Revue ESAIM: Probability and Statistics Année : 2020

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

Résumé

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.
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Dates et versions

hal-04510342 , version 1 (18-03-2024)

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A. Gloter, I. Honoré, Dasha Loukianova. Approximation of the invariant distribution for a class of ergodic jump diffusions. ESAIM: Probability and Statistics, 2020, 24, pp.883-913. ⟨10.1051/ps/2020023⟩. ⟨hal-04510342⟩
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