Precise deviations for Hawkes processes

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.

31 pages, 2 tables

References in corpus (3)

• Robust dynamic classes revealed by measuring the response function of a social system
• Functional central limit theorems for stationary Hawkes processes and application to infinite-server queues
• Scaling limits for Hawkes processes and application to financial statistics

Cited by in corpus (2)

• Precise deviations for Cox processes with a shot noise intensity
• Some asymptotic results for nonlinear Hawkes processes