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).
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Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2017, 22 (42), 〈10.1214/17-EJP63〉
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Julien Chevallier. Fluctuations for mean-field interacting age-dependent Hawkes processes. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2017, 22 (42), 〈10.1214/17-EJP63〉. 〈hal-01393373v2〉

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