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

Published online by Cambridge University Press:  30 January 2018

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: [email protected]
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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.

Type
Research Article
Copyright
© Applied Probability Trust 

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