Fluctuations for mean-field interacting age-dependent Hawkes processes

Abstract : The propagation of chaos and associated law of large numbers for mean-field interacting age-dependent Hawkes processes (when the number of processes n goes to +∞) being granted by the study performed in (Chevallier, 2015), the aim of the present paper is to prove the resulting functional central limit theorem. It involves the study of a measure-valued process describing the fluctuations (at scale n −1/2) of the empirical measure of the ages around its limit value. This fluctuation process is proved to converge towards a limit process characterized by a limit system of stochastic differential equations driven by a Gaussian noise instead of Poisson (which occurs for the law of large numbers limit).
Type de document :
Pré-publication, Document de travail
2016
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https://hal.archives-ouvertes.fr/hal-01393373
Contributeur : Julien Chevallier <>
Soumis le : lundi 7 novembre 2016 - 13:02:43
Dernière modification le : mardi 8 novembre 2016 - 01:01:06
Document(s) archivé(s) le : mercredi 8 février 2017 - 14:01:12

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Fluc_HP_v1.pdf
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Distributed under a Creative Commons Paternité - Pas d'utilisation commerciale 4.0 International License

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  • HAL Id : hal-01393373, version 1
  • ARXIV : 1611.02008

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Julien Chevallier. Fluctuations for mean-field interacting age-dependent Hawkes processes. 2016. <hal-01393373>

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