Limit theorems for a jump-diffusion model with Hawkes jumps

Abstract

We consider a jump-diffusion process with Hawkes jumps which has
been widely applied in insurance, finance, queue theory, statistic,
and many other fields. This model can be compared with the
Poissonian jump-diffusion model familiar to financial economists
since Merton~\cite{Merton}. We study the limit theorems for a
jump-diffusion process with Hawkes jumps. In particular, we obtain a
law of large number, central limit theorems, and large deviations
principle. In addition, we give some examples for random variable
$Y_{1}$ to find quantities of several limit behaviors.