Asymptotics for an extended inverse Markovian Hawkes process
J. Korean Math. Soc.
Published online November 24, 2020
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
and has been widely applied in insurance, finance, queue theory,
statistic, 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 an Hawkes process and inverse
Markovian Hawkes process that 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 with several key results.
Keywords : Hawkes process, Inverse Markovian, Self-exciting point processes, Central limit theorems, Law of Large Numbers.
MSC numbers : 60G55, 60F05, 60F10
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