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http://dx.doi.org/10.4134/JKMS.j180483

LIMIT THEOREMS FOR HAWKES PROCESSES WITH UNIFORM IMMIGRANTS  

Seol, Youngsoo (Department of Mathematics Dong-A University)
Publication Information
Journal of the Korean Mathematical Society / v.56, no.4, 2019 , pp. 935-946 More about this Journal
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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