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Functional central limit theorems and moderate deviations for Poisson cluster processes

Part of: Limit theorems Stochastic processes

Published online by Cambridge University Press:  24 September 2020

Fuqing Gao  and
Yujing Wang
Fuqing Gao*
Affiliation:
Wuhan University
Yujing Wang*
Affiliation:
Wuhan University
*
*Postal address: School of Mathematics and Statistics, Wuhan University, Wuhan430072, China. Email: fqgao@whu.edu.cn
**Postal address: School of Mathematics and Statistics, Wuhan University, Wuhan430072, China. Email: yujingwang@whu.edu.cn
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Abstract

In this paper, we consider functional limit theorems for Poisson cluster processes. We first present a maximal inequality for Poisson cluster processes. Then we establish a functional central limit theorem under the second moment and a functional moderate deviation principle under the Cramér condition for Poisson cluster processes. We apply these results to obtain a functional moderate deviation principle for linear Hawkes processes.

Keywords

Poisson cluster processHawkes processmaximal inequalitycentral limit theoremmoderate deviationlarge deviation

MSC classification

Primary: 60F10: Large deviations 60F17: Functional limit theorems; invariance principles 60G55: Point processes
Type
Original Article
Information
Advances in Applied Probability , Volume 52 , Issue 3 , September 2020 , pp. 916 - 941
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Copyright
© Applied Probability Trust 2020

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