Limit theorems for Hawkes processes with uniform immigrants
J. Korean Math. Soc.
Published online 2019 Feb 01
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 law of large numbers, a central
limit theorems, and large deviations principle.
Keywords : Hawkes process, Uniform immigrants, Self-exciting point processes, Law of Large Numbers, Central limit theorems, Large deviations principle
MSC numbers : 60G55, 60F05, 60F10
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