ON THE LONGEST RUNS IN MARKOV CHAINS

被引：3

作者：

Liu, Zhenxia ^{[1
]}

Yang, Xiangfeng ^{[1
]}

机构：

[1] Linkoping Univ, Dept Math, S-58183 Linkoping, Sweden

来源：

PROBABILITY AND MATHEMATICAL STATISTICS-POLAND | 2018年 / 38卷 / 02期

关键词：

Longest run; moment generating function; large deviation principle; Markov chain; CONFIDENCE-INTERVALS; SEQUENCE;

D O I：

10.19195/0208-4147.38.2.8

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 the first n steps of a two-state (success and failure) Markov chain, the longest success run L(n) has been attracting considerable attention due to its various applications. In this paper, we study L(n) in terms of its two closely connected properties: moment generating function and large deviations. This study generalizes several existing results in the literature, and also finds an application in statistical inference. Our method on the moment generating function is based on a global estimate of the cumulative distribution function of L(n) proposed in this paper, and the proofs of the large deviations include the Gartner-Ellis theorem and the moment generating function.

引用

页码：407 / 428

页数：22

共 14 条

[1]

BALAKRISHNAN N., 2002, Runs and Scans with Applications

[2] APPROXIMATE CONFIDENCE-INTERVALS FOR THE PARAMETERS OF A STATIONARY BINARY MARKOV-CHAIN [J].