Renewal Time Points for Hawkes Processes
Probability
2019-06-11 v2
Abstract
In the last decade Hawkes processes have received much attention as models for functional connectivity in neural spiking networks and other dynamical systems with a cascade behavior. In this paper we establish a renewal approach for analyzing this process. We consider the ordinary nonlinear Hawkes process as well as the more recently described age dependent Hawkes process. We construct renewal-times and establish moment results for these. This gives rise to study the Hawkes process as a Markov chain. As an application, we prove asymptotic results such as a functional CLT and a time-average CLT.
Keywords
Cite
@article{arxiv.1906.02036,
title = {Renewal Time Points for Hawkes Processes},
author = {Mads Bonde Raad},
journal= {arXiv preprint arXiv:1906.02036},
year = {2019}
}