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Limit Theorems for a Cox-Ingersoll-Ross Process with Hawkes Jumps

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: School of Mathematics, University of Minnesota - Twin Cities, 206 Church Street S. E., Minneapolis, MN-55455, USA. Email address: ling@cims.nyu.edu
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Abstract

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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.

Keywords

Cox-Ingersoll-Ross processpoint processHawkes processself-exciting processcentral limit theoremlarge deviations

MSC classification

Primary: 60G07: General theory of processes 60G55: Point processes 60F05: Central limit and other weak theorems 60F10: Large deviations
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 3 , September 2014 , pp. 699 - 712
Copyright
© Applied Probability Trust 

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