GAUSSIAN APPROXIMATION OF NONLINEAR HAWKES PROCESSES

• 成果类型: Article
• 署名作者: Torrisi, Giovanni Luca
• 署名单位: Consiglio Nazionale delle Ricerche (CNR); Istituto per le Applicazioni del Calcolo Mauro Picone (IAC-CNR)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/15-AAP1141
• 发表日期: 2016
• 页码: 2106-2140
• 关键词: point-processes; LIMIT-THEOREMS; Poisson processes; large deviations; simulation; REPRESENTATION; CONVERGENCE; STABILITY; SPECTRA

摘要

We give a general Gaussian bound for the first chaos (or innovation) of point processes with stochastic intensity constructed by embedding in a bivariate Poisson process. We apply the general result to nonlinear Hawkes processes, providing quantitative central limit theorems.