J. Korean Math. Soc. 2021; 58(4): 819-833
Online first article November 24, 2020 Printed July 1, 2021
https://doi.org/10.4134/JKMS.j200251
Copyright © The Korean Mathematical Society.
Youngsoo Seol
Dong-A University
Hawkes process is a self-exciting simple point process with clustering effect whose jump rate depends on its entire past history and has been widely applied in insurance, finance, queueing theory, statistics, and many other fields. Seol~\cite{Seol5} proposed the inverse Markovian Hawkes processes and studied some asymptotic behaviors. In this paper, we consider an extended inverse Markovian Hawkes process which combines a Markovian Hawkes process and inverse Markovian Hawkes process with features of several existing models of self-exciting processes. We study the limit theorems for an extended inverse Markovian Hawkes process. In particular, we obtain a law of large number and central limit theorems.
Keywords: Hawkes process, inverse Markovian, self-exciting point processes, central limit theorems, law of large numbers
MSC numbers: Primary 60G55, 60F05, 60F10
Supported by: This research is supported by the Dong-A University research grant.
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