Open Access
2017 Fluctuations for mean-field interacting age-dependent Hawkes processes
Julien Chevallier
Electron. J. Probab. 22: 1-49 (2017). DOI: 10.1214/17-EJP63


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 $+\infty $) being granted by the study performed in [9], 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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Julien Chevallier. "Fluctuations for mean-field interacting age-dependent Hawkes processes." Electron. J. Probab. 22 1 - 49, 2017.


Received: 7 November 2016; Accepted: 27 April 2017; Published: 2017
First available in Project Euclid: 3 May 2017

zbMATH: 1364.60062
MathSciNet: MR3646068
Digital Object Identifier: 10.1214/17-EJP63

Primary: 60F05 , 60G55 , 60G57 , 60H15 , 92B20

Keywords: central limit theorem , Hawkes process , interacting particle systems , neural network , Stochastic partial differential equation

Vol.22 • 2017
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