Functional Limit Theorems for Marked Hawkes Point Measures
Probability
2019-08-20 v1
Abstract
This paper establishes a functional law of large numbers and a functional central limit theorem for marked Hawkes point measures and their corresponding shot noise processes. We prove that the normalized random measure can be approximated in distribution by the sum of a Gaussian white noise process plus an appropriate lifting map of a correlated one-dimensional Brownian motion. The Brownian results from the self-exiting arrivals of events. We apply our limit theorems for Hawkes point measures to analyze the population dynamics of budding microbes in a host.
Cite
@article{arxiv.1908.06703,
title = {Functional Limit Theorems for Marked Hawkes Point Measures},
author = {Ulrich Horst and Wei Xu},
journal= {arXiv preprint arXiv:1908.06703},
year = {2019}
}