Journal of Applied Probability

Central limit theorem for nonlinear Hawkes processes

Lingjiong Zhu

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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.

Article information

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

First available in Project Euclid: 5 September 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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

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