Functional limit theorems for marked Hawkes point measures

Ulrich Horst and Wei Xu

Stochastic Processes and their Applications, 2021, vol. 134, issue C, 94-131

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 motion results from the self-exciting arrivals of events. We apply our limit theorems for Hawkes point measures to analyze the population dynamics of budding microbes in a host as well as their interaction with that host.

Keywords: Hawkes point measure; Marked Hawkes process; Functional limit theorem; Budding microbes in a host (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spa.2020.12.002

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