Limit theorems for Hawkes processes with uniform immigrants
J. Korean Math. Soc. 2019 Vol. 56, No. 4, 935-946
Published online July 1, 2019
Youngsoo Seol
Dong-A University
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
MSC numbers : Primary 60G55; Secondary 60F05, 60F10
Supported by : This research is supported by the Dong-A University research grant.
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