Large and moderate deviations for the total population in the nearly unstable INAR(1) model

被引：1
|
作者：
Li, Shimin [1 ]
Jiang, Hui [1 ]
Wang, Shaochen [2 ]
机构：
[1] Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing 210016, Jiangsu, Peoples R China
[2] South China Univ Technol, Sch Math, Guangzhou, Guangdong, Peoples R China
来源：
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS | 2018年 / 47卷 / 07期
基金：
中国博士后科学基金; 中国国家自然科学基金;
关键词：
INAR model; large deviations; moderate deviations; 60J80; 60F10; 62G20; BRANCHING-PROCESS; IMMIGRATION;
D O I：
10.1080/03610926.2017.1324988
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：
This paper considers the non negative integer-valued autoregressive process with order one (INAR(1)), where the autoregression parameter is close to unity. Using the methods introduced by Yu, Wang, and Chen (2016), the large and moderate deviations with explicit rate functions for the total population of this process can be obtained.
引用
收藏
页码：1718 / 1730
页数：13
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    [J]. JOURNAL OF APPLIED PROBABILITY, 2003, 40 (03) : 750 - 765
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  • [6] Poisson limit of an inhomogeneous nearly critical INAR(1) model
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