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.
Citation
Lingjiong Zhu. "Limit theorems for a Cox-Ingersoll-Ross process with Hawkes jumps." J. Appl. Probab. 51 (3) 699 - 712, September 2014. https://doi.org/10.1239/jap/1409932668
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