Journal of the
Korean Mathematical Society JKMS

Hawkes process is a self-exciting simple point process with clustering effect whose jump rate depends on its entire past history. We consider Hawkes processes with uniform immigrants which is a special case of the Hawkes processes with renewal immigrants. We study the limit theorems for Hawkes processes with uniform immigrants. In particular, we obtain a law of large number, a central limit theorem, and a large deviation principle.

Keywords: Hawkes process, uniform immigrants, self-exciting point processes, law of large numbers, central limit theorems, large deviations principle

MSC numbers: Primary 60G55; Secondary 60F05, 60F10

Supported by: This research is supported by the Dong-A University research grant.