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Central Limit Theorem for Nonlinear Hawkes Processes

Part of: Stochastic processes Limit theorems

Published online by Cambridge University Press:  30 January 2018

Lingjiong Zhu
Lingjiong Zhu*
Affiliation:
New York University
*
∗ Postal address: Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY-10012, USA. Email address: ling@cims.nyu.edu
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Abstract

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The Hawkes process is a self-exciting point process with clustering effect whose intensity depends on its entire past history. It has wide applications in neuroscience, finance, and many other fields. In this paper we obtain a functional central limit theorem for the nonlinear Hawkes process. Under the same assumptions, we also obtain a Strassen's invariance principle, i.e. a functional law of the iterated logarithm.

Keywords

Central limit theoremfunctional central limit theorempoint processHawkes processself-exciting process

MSC classification

Primary: 60G55: Point processes 60F05: Central limit and other weak theorems
Type
Research Article
Information
Journal of Applied Probability , Volume 50 , Issue 3 , September 2013 , pp. 760 - 771
Copyright
© Applied Probability Trust 

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