# LIMIT THEOREMS FOR HAWKES PROCESSES WITH UNIFORM IMMIGRANTS

Seol, Youngsoo

• Received : 2018.07.19
• Accepted : 2018.11.21
• Published : 2019.07.01
• 46 3

#### Abstract

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

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#### Acknowledgement

Supported by : Dong-A University