Large deviations and applications for Markovian Hawkes processes with a large initial intensity
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AbstractHawkes process is a class of simple point processes that is self-exciting and has clustering effect. The intensity of this point process depends on its entire past history. It has wide applications in finance, insurance, neuroscience, social networks, criminology, seismology, and many other fields. In this paper, we study linear Hawkes process with an exponential kernel in the asymptotic regime where the initial intensity of the Hawkes process is large. We establish large deviations for Hawkes processes in this regime as well as the regime when both the initial intensity and the time are large. We illustrate the strength of our results by discussing the applications to insurance and queueing systems.
Acceptance Date11/04/2017
All Author(s) ListXuefeng Gao, Lingjiong Zhu
Journal nameBernoulli
Year2018
Month11
Volume Number24
Issue Number4A
PublisherBernoulli Society for Mathematical Statistics and Probability
Pages2875 - 2905
ISSN1350-7265
eISSN1573-9759
LanguagesEnglish-United States