Moderate deviations for empirical measures of Markov chains: Upper bounds

被引：25

作者：

de Acosta, A ^{[1
]}

Chen, X ^{[1
]}

机构：

[1] Case Western Reserve Univ, Dept Math, Cleveland, OH 44106 USA

来源：

JOURNAL OF THEORETICAL PROBABILITY | 1998年 / 11卷 / 04期

基金：

美国国家科学基金会;

关键词：

empirical measures; Markov chains; geometric ergodicity; moderate deviations; regeneration-split chain method; projective system;

D O I：

10.1023/A:1022673000778

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：

We obtain upper bounds for moderate deviations of empirical measures of Markov chains with general state space in the tau-topology under the minimal assumption of geometric ergodicity. The regeneration-split chain method and a result on projective systems are employed in the proof.

引用

页码：1075 / 1110

页数：36

共 20 条

[1]

[Anonymous], 1992, Stochastic Stability of Markov chains

[2] NEW APPROACH TO THE LIMIT THEORY OF RECURRENT MARKOV-CHAINS [J].

ATHREYA, KB ;

NEY, P .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1978, 245 (NOV) :493-501

[3]

Chen X., 1991, CHINESE J APPL PROBA, V7, P24

[4]

CHEN X, 1996, IN PRESS MEMOIRS AMS

[5]

Chung K. L., 1967, MARKOV CHAINS STATIO

[6]

de Acosta A, 1997, ANN PROBAB, V25, P259

[7]

de Acosta A., 1997, Festschrift for Lucien Le Cam, P143, DOI [10.1007/978-1-4612-1880-79, 10.1007/978-1-4612-1880-7_9, DOI 10.1007/978-1-4612-1880-7_9]

[8] LARGE DEVIATIONS FOR VECTOR-VALUED FUNCTIONALS OF A MARKOV-CHAIN - LOWER BOUNDS [J].

DEACOSTA, A .

ANNALS OF PROBABILITY, 1988, 16 (03) :925-960

[9]

DEACOSTA A, 1992, T AM MATH SOC, V329, P357

[10]

Dembo A., 1993, Large deviations techniques and applications

← 1 2 →