FUNCTIONAL CENTRAL LIMIT THEOREMS AND MODERATE DEVIATIONS FOR POISSON CLUSTER PROCESSES

被引：4

作者：

Gao, Fuqing ^{[1
]}

Wang, Yujing ^{[1
]}

机构：

[1] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China

来源：

ADVANCES IN APPLIED PROBABILITY | 2020年 / 52卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Poisson cluster process; Hawkes process; maximal inequality; central limit theorem; moderate deviation; large deviation; HAWKES PROCESSES; INPUT PROCESS; APPROXIMATION; PREDICTION; NETWORKS;

D O I：

10.1017/apr.2020.25

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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 Cramer condition for Poisson cluster processes. We apply these results to obtain a functional moderate deviation principle for linear Hawkes processes.

引用

页码：916 / 941

页数：26

共 28 条

[1] [Anonymous], 1986, Probability and Measure
[2] Some limit theorems for Hawkes processes and application to financial statistics
Bacry, E.
Delattre, S.
Hoffmann, M.
Muzy, J. F.
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2013, 123 (07) : 2475 - 2499
[3] Billingsley P., 2013, Convergence of Probability Measures, DOI DOI 10.1002/9780470316962
[4] Poisson cluster measures: Quasi-invariance, integration by parts and equilibrium stochastic dynamics
Bogachev, Leonid
Daletskii, Alexei
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2009, 256 (02) : 432 - 478
[5] Large deviations of poisson cluster processes
Bordenave, Charles
Torrisi, Giovanni Luea
[J]. STOCHASTIC MODELS, 2007, 23 (04) : 593 - 625
[6] Modeling Heterogeneous Cellular Networks Interference Using Poisson Cluster Processes
Chun, Young Jin
Hasna, Mazen O.
Ghrayeb, Ali
[J]. IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, 2015, 33 (10) : 2182 - 2195
[7] Daley D., 2003, INTRO THEORY POINT P
[8] HAWKES PROCESSES ON LARGE NETWORKS
Delattre, Sylvain
Fournier, Nicolas
Hoffmann, Marc
[J]. ANNALS OF APPLIED PROBABILITY, 2016, 26 (01) : 216 - 261
[9] Dembo A., 2010, Large Deviations Techniques and Applications
[10] Djellout H., 1999, Statistical Inference for Stochastic Processes, V2, P195

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