NON-ASYMPTOTIC CONCENTRATION INEQUALITY FOR AN APPROXIMATION OF THE INVARIANT DISTRIBUTION OF A DIFFUSION DRIVEN BY COMPOUND POISSON PROCESS - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2018

NON-ASYMPTOTIC CONCENTRATION INEQUALITY FOR AN APPROXIMATION OF THE INVARIANT DISTRIBUTION OF A DIFFUSION DRIVEN BY COMPOUND POISSON PROCESS

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, particularly suitable in cases where the driving Lévy process is a Compound Poisson. This scheme is similar to those introduced by Lamberton and Pagès in [LP02] for a Brownian diffusion and extended by Panloup in [Pan08b] to the Jump Diffusion with Lévy jumps. We obtain a non-asymptotic Gaussian concentration bound for the difference between the invariant distribution and the empirical distribution computed with the scheme of decreasing time step along a appropriate test functions f such that f − ν(f) is is a coboundary of the infinitesimal generator.
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Dates et versions

hal-01885479 , version 1 (01-10-2018)

Identifiants

  • HAL Id : hal-01885479 , version 1

Citer

Arnaud Gloter, Igor Honoré, Dasha Loukianova. NON-ASYMPTOTIC CONCENTRATION INEQUALITY FOR AN APPROXIMATION OF THE INVARIANT DISTRIBUTION OF A DIFFUSION DRIVEN BY COMPOUND POISSON PROCESS. 2018. ⟨hal-01885479⟩
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