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

Abstract : 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.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-01885479
Contributor : Igor Honoré <>
Submitted on : Monday, October 1, 2018 - 11:33:08 PM
Last modification on : Tuesday, May 14, 2019 - 12:46:01 PM
Long-term archiving on : Wednesday, January 2, 2019 - 3:33:26 PM

Identifiers

  • HAL Id : hal-01885479, version 1

Citation

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⟩

Share

Metrics

Record views

201

Files downloads

65