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2019 Asymptotics for Hawkes processes with large and small baseline intensities
Youngsoo Seol
Rocky Mountain J. Math. 49(2): 661-680 (2019). DOI: 10.1216/RMJ-2019-49-2-661


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.

Funding Statement

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


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Youngsoo Seol. "Asymptotics for Hawkes processes with large and small baseline intensities." Rocky Mountain J. Math. 49 (2) 661 - 680, 2019.


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

zbMATH: 07079990
MathSciNet: MR3973246
Digital Object Identifier: 10.1216/RMJ-2019-49-2-661

Primary: 60G55
Secondary: 60F05 , 60F10}

Keywords: central limit theorems , Hawkes processes , intensity process , large deviations , Law of Large Numbers , Moderate deviations

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium


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Vol.49 • No. 2 • 2019
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