Journal of Applied Probability

Limit theorems for a Cox-Ingersoll-Ross process with Hawkes jumps

Lingjiong Zhu

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In this paper we propose a stochastic process, which is a Cox-Ingersoll-Ross process with Hawkes jumps. It can be seen as a generalization of the classical Cox-Ingersoll-Ross process and the classical Hawkes process with exponential exciting function. Our model is a special case of the affine point processes. We obtain Laplace transforms and limit theorems, including the law of large numbers, central limit theorems, and large deviations.

Article information

J. Appl. Probab., Volume 51, Number 3 (2014), 699-712.

First available in Project Euclid: 5 September 2014

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Zentralblatt MATH identifier

Primary: 60G07: General theory of processes 60G55: Point processes 60F05: Central limit and other weak theorems 60F10: Large deviations

Cox-Ingersoll-Ross process point process Hawkes process self-exciting process central limit theorem large deviations


Zhu, Lingjiong. Limit theorems for a Cox-Ingersoll-Ross process with Hawkes jumps. J. Appl. Probab. 51 (2014), no. 3, 699--712. doi:10.1239/jap/1409932668.

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