DIFFUSIVE LIMITS OF LIPSCHITZ FUNCTIONALS OF POISSON MEASURES

• 成果类型: Article
• 署名作者: Besancon, Eustache; Coutin, Laure; Decreusefond, Laurent; Moyal, Pascal
• 署名单位: IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite de Lorraine
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/23-AAP1972
• 发表日期: 2024
• 页码: 555-584
• 关键词: Gaussian Approximation; steins method; hawkes; CONVERGENCE

摘要

Continuous time Markov Chains, Hawkes processes and many other interesting processes can be described as a 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 toward 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 diffusive limits of Markov processes and long-time behavior of Hawkes processes.