Functional Limit Theorems for Marked Hawkes Point Measures *

Ulrich Horst and Wei Xu ()
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Ulrich Horst: Institut für Mathematik [Berlin] - TUB - Technical University of Berlin / Technische Universität Berlin
Wei Xu: Institut für Mathematik [Berlin] - TUB - Technical University of Berlin / Technische Universität Berlin

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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 wihte 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.

Keywords: Hawkes point measure; marked Hawkes process; functional limit theorem; budding microbes in a host (search for similar items in EconPapers)
Date: 2019-08-17
Note: View the original document on HAL open archive server: https://univ-lemans.hal.science/hal-02443841
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