Limit theorems for Hawkes processes with uniform immigrants
J. Korean Math. Soc. 2019 Vol. 56, No. 4, 935-946
https://doi.org/10.4134/JKMS.j180483
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
Full-Text :

   

Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang.co., Ltd