Limit Theorems for Linear Markovian Hawkes Processes with Large Intensity
Hawkes process has been used to model security order arrivals in high-frequency finance. It is a self-exciting point process with clustering effect whose jump intensity depends on its entire past history. In this paper, we study linear Hawkes process with an exponential kernel in the asymptotic regime where the initial intensity of the Hawkes process is large. We derive limit theorems for this asymptotic regime as well as the case when both the initial intensity and the time are large.
This is joint work with Lingjiong Zhu from Florida State University.