Diffusive limits of Lipschitz functionals of Poisson measures - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year :

Diffusive limits of Lipschitz functionals of Poisson measures

(1, 2, 3) , (4) , (1, 2, 3) , (5, 6)
1
2
3
4
5
6

Abstract

Continuous Time Markov Chains, Hawkes processes and many other interesting processes can be described as solution of stochastic differential equations driven by Poisson measures. Previous works, using the Stein's method, give the convergence rate of a sequence of renormalized Poisson measures towards the Brownian motion in several distances, constructed on the model of the Kantorovitch-Rubinstein (or Wasserstein-1) distance. We show that many operations (like time change, convolution) on continuous functions are Lipschitz continuous to extend these quantified convergences to diffuse limits of Markov processes and long-time behavior of Hawkes processes.

Keywords

Fichier principal
Vignette du fichier
stability_hal.pdf (277.82 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03283778 , version 1 (12-07-2021)
hal-03283778 , version 2 (15-12-2022)

Identifiers

  • HAL Id : hal-03283778 , version 1

Cite

Eustache Besançon, Laure Coutin, Laurent Decreusefond, Pascal Moyal. Diffusive limits of Lipschitz functionals of Poisson measures. 2021. ⟨hal-03283778v1⟩

Collections

IECLPS
114 View
40 Download

Share

Gmail Facebook Twitter LinkedIn More