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Pré-Publication, Document De Travail Année : 2019

Functional Limit Theorems for Marked Hawkes Point Measures *

Ulrich Horst
Wei Xu
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Résumé

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.
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Dates et versions

hal-02443841 , version 1 (17-01-2020)

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  • HAL Id : hal-02443841 , version 1

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Ulrich Horst, Wei Xu. Functional Limit Theorems for Marked Hawkes Point Measures *. 2019. ⟨hal-02443841⟩

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