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Large Deviations And Applications For Markovian Hawkes Processes With A Large Initial Intensity

Title: Large Deviations And Applications For Markovian Hawkes Processes With A Large Initial Intensity.
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Name(s): Gao, Xuefeng, author
Zhu, Lingjiong, author
Type of Resource: text
Genre: Journal Article
Text
Journal Article
Date Issued: 2018-11-01
Physical Form: computer
online resource
Extent: 1 online resource
Language(s): English
Abstract/Description: Hawkes 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.
Identifier: FSU_libsubv1_wos_000429696200015 (IID), 10.3150/17-BEJ948 (DOI)
Keywords: spectra, risk, approximation, claims, ruin, exciting point-processes, Hawkes processes, limit-theorems, insurance, large deviations, large initial intensity, queueing systems
Publication Note: The publisher’s version of record is available at https://doi.org/10.3150/17-BEJ948
Persistent Link to This Record: http://purl.flvc.org/fsu/fd/FSU_libsubv1_wos_000429696200015
Owner Institution: FSU
Is Part Of: Bernoulli.
1350-7265
Issue: iss. 4A, vol. 24

Choose the citation style.
Gao, X., & Zhu, L. (2018). Large Deviations And Applications For Markovian Hawkes Processes With A Large Initial Intensity. Bernoulli. Retrieved from http://purl.flvc.org/fsu/fd/FSU_libsubv1_wos_000429696200015