• Bernoulli
  • Volume 24, Number 4A (2018), 2875-2905.

Large deviations and applications for Markovian Hawkes processes with a large initial intensity

Xuefeng Gao and Lingjiong Zhu

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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.

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Bernoulli, Volume 24, Number 4A (2018), 2875-2905.

Received: April 2016
Revised: February 2017
First available in Project Euclid: 26 March 2018

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Hawkes processes insurance large deviations large initial intensity queueing systems


Gao, Xuefeng; Zhu, Lingjiong. Large deviations and applications for Markovian Hawkes processes with a large initial intensity. Bernoulli 24 (2018), no. 4A, 2875--2905. doi:10.3150/17-BEJ948.

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Supplemental materials

  • Supplement to “Large deviations and applications for Markovian Hawkes processes with a large initial intensity”. We provide proofs for additional results in the paper in the supplemental article [14].