Precise deviations for Hawkes processes

Fuqing Gao; Lingjiong Zhu

doi:10.3150/20-BEJ1235

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Home > Journals > Bernoulli > Volume 27 > Issue 1 > Article

February 2021 Precise deviations for Hawkes processes

Fuqing Gao, Lingjiong Zhu

Bernoulli 27(1): 221-248 (February 2021). DOI: 10.3150/20-BEJ1235

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Abstract

Hawkes process is a class of simple point processes with self-exciting and clustering properties. Hawkes process has been widely applied in finance, neuroscience, social networks, criminology, seismology, and many other fields. In this paper, we study precise deviations for Hawkes processes for large time asymptotics, that strictly extends and improves the existing results in the literature. Numerical illustrations will also be provided.