Journal of Applied Probability

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

Lingjiong Zhu

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Abstract

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

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

Dates
First available in Project Euclid: 5 September 2014

Permanent link to this document
https://projecteuclid.org/euclid.jap/1409932668

Digital Object Identifier
doi:10.1239/jap/1409932668

Mathematical Reviews number (MathSciNet)
MR3256221

Zentralblatt MATH identifier
1307.60033

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

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

Citation

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. https://projecteuclid.org/euclid.jap/1409932668


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