Gaussian approximation of nonlinear Hawkes processes

Abstract

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.

Published at http://dx.doi.org/10.1214/15-AAP1141 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (5)

• Adaptive estimation for Hawkes processes; application to genome analysis
• Central limit theorems for $U$-statistics of Poisson point processes
• Limit theorems for nearly unstable Hawkes processes
• Statistical Distributions of Earthquake Numbers: Consequence of Branching Process
• Large deviations for Markovian nonlinear Hawkes processes

Cited by in corpus (4)

• Hybrid marked point processes: characterisation, existence and uniqueness
• Diffusive limits of Lipschitz functionals of Poisson measures
• Normal approximation of Kabanov-Skorohod integrals on Poisson spaces
• Gaussian Approximation and Moderate Deviations of Poisson Shot Noises with Application to Compound Generalized Hawkes Processes