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..
| Original language | English (US) |
|---|---|
| Pages (from-to) | 699-712 |
| Number of pages | 14 |
| Journal | Journal of Applied Probability |
| Volume | 51 |
| Issue number | 3 |
| DOIs | |
| State | Published - Sep 1 2014 |
Bibliographical note
Publisher Copyright:© 2014 Applied Probability Trust.
Keywords
- Central limit theorem
- Cox-Ingersoll-Ross process
- Hawkes process
- Large deviations
- Point process
- Self-exciting process