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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DOI : 10.1051/ps/2020023
Keywords: Invariant distribution, diffusion processes, jump processes, inhomogeneous Markov chains, non-asymptotic Gaussian concentration
@article{PS_2020__24_1_883_0,
author = {Gloter, A. and Honor\'e, I. and Loukianova, D.},
title = {Approximation of the invariant distribution for a class of ergodic jump diffusions},
journal = {ESAIM: Probability and Statistics},
pages = {883--913},
year = {2020},
publisher = {EDP Sciences},
volume = {24},
doi = {10.1051/ps/2020023},
mrnumber = {4178367},
zbl = {1455.60091},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ps/2020023/}
}
TY - JOUR AU - Gloter, A. AU - Honoré, I. AU - Loukianova, D. TI - Approximation of the invariant distribution for a class of ergodic jump diffusions JO - ESAIM: Probability and Statistics PY - 2020 SP - 883 EP - 913 VL - 24 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/ps/2020023/ DO - 10.1051/ps/2020023 LA - en ID - PS_2020__24_1_883_0 ER -
%0 Journal Article %A Gloter, A. %A Honoré, I. %A Loukianova, D. %T Approximation of the invariant distribution for a class of ergodic jump diffusions %J ESAIM: Probability and Statistics %D 2020 %P 883-913 %V 24 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/ps/2020023/ %R 10.1051/ps/2020023 %G en %F PS_2020__24_1_883_0
Gloter, A.; Honoré, I.; Loukianova, D. Approximation of the invariant distribution for a class of ergodic jump diffusions. ESAIM: Probability and Statistics, Tome 24 (2020), pp. 883-913. doi: 10.1051/ps/2020023
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