Approximation of the invariant distribution for a class of ergodic jump diffusions
| Autor: | Igor Honoré, Dasha Loukianova, Arnaud Gloter |
|---|---|
| Přispěvatelé: | Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE) |
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Gaussian 010102 general mathematics Mathematical analysis Jump diffusion diffusion processes 01 natural sciences Empirical distribution function 010104 statistics & probability symbols.namesake non-asymptotic Gaussian concentration Compound Poisson process symbols Ergodic theory Infinitesimal generator inhomogeneous Markov chains [MATH]Mathematics [math] 0101 mathematics Invariant (mathematics) Invariant distribution jump processes Brownian motion Mathematics |
| Zdroj: | ESAIM: Probability and Statistics ESAIM: Probability and Statistics, EDP Sciences, 2020, 24, pp.883-913. ⟨10.1051/ps/2020023⟩ ESAIM: Probability and Statistics, 2020, 24, pp.883-913. ⟨10.1051/ps/2020023⟩ |
| ISSN: | 1262-3318 1292-8100 |
| DOI: | 10.1051/ps/2020023 |
| Popis: | In this article, we approximate the invariant distributionνof 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 PagèsBernoulli8(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-asymptoticquasiGaussian (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 functionsfsuch thatf−ν(f) is a coboundary of the infinitesimal generator. |
| Databáze: | OpenAIRE |
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