Journal of Applied Probability

Central limit theorem for nonlinear Hawkes processes

Lingjiong Zhu

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Abstract

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.

Article information

Source
J. Appl. Probab., Volume 50, Number 3 (2013), 760-771.

Dates
First available in Project Euclid: 5 September 2013

Permanent link to this document
https://projecteuclid.org/euclid.jap/1378401234

Digital Object Identifier
doi:10.1239/jap/1378401234

Mathematical Reviews number (MathSciNet)
MR3102513

Zentralblatt MATH identifier
1306.60015

Subjects
Primary: 60G55: Point processes 60F05: Central limit and other weak theorems

Keywords
Central limit theorem functional central limit theorem point process Hawkes process self-exciting process

Citation

Zhu, Lingjiong. Central limit theorem for nonlinear Hawkes processes. J. Appl. Probab. 50 (2013), no. 3, 760--771. doi:10.1239/jap/1378401234. https://projecteuclid.org/euclid.jap/1378401234


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