Rocky Mountain Journal of Mathematics

Asymptotics for Hawkes processes with large and small baseline intensities

Youngsoo Seol

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This paper focuses on asymptotic results for linear Hawkes processes with large and small baseline intensities. The intensity process is one of the main tools used to work with the dynamical properties of a general point process. It is of essential interest in credit risk study, in particular. First, we establish a large deviation principle and a moderate deviation principle for the Hawkes process with large baseline intensity. In addition, a law of large numbers and a central limit theorem are also obtained. Second, we observe asymptotic behaviors for the Hawkes process with small baseline intensity. The main idea of the proof relies on the immigration-birth representation and the observations of the moment generating function for the linear Hawkes process.


This research was supported from a Dong-A University research grant.

Article information

Rocky Mountain J. Math., Volume 49, Number 2 (2019), 661-680.

Received: 31 May 2017
Revised: 3 October 2018
First available in Project Euclid: 23 June 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G55: Point processes
Secondary: 60F05: Central limit and other weak theorems 60F10}

Hawkes processes intensity process central limit theorems law of large numbers large deviations moderate deviations


Seol, Youngsoo. Asymptotics for Hawkes processes with large and small baseline intensities. Rocky Mountain J. Math. 49 (2019), no. 2, 661--680. doi:10.1216/RMJ-2019-49-2-661.

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