The functional moderate deviations for Harris recurrent Markov chains and applications

被引：9

作者：

Chen, X

Guillin, A ^{[1
]}

机构：

[1] Univ Tennessee, Dept Math, Knoxville, TN 37996 USA

[2] Univ Paris 09, CEREMADE, F-75775 Paris 16, France

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2004年 / 40卷 / 01期

基金：

美国国家科学基金会;

关键词：

Harris recurrent Markov chain; p-regularity; moderate deviation; the law of the iterated logarithm;

D O I：

10.1016/j.anihpb.2003.07.002

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 study exponentially asymptotic behaviors for the trajectories of additive functionals of Harris Markov chains. In the main result, we establish a moderate deviation principle for a pair of additive functionals of different growth rates. Moreover, we give explicit formulas for the rate functions which exhibit a non-quadratic behavior. In particular, we achieve the functional moderate deviations in two different scales. As an application, we obtain a functional law of LIL, which leads to a variety of strong limit laws in the spirit of Strassen [Z. Wahr. Geb. 3 (1964) 211-226]. (C) 2003 Elsevier SAS. All rights reserved.

引用

页码：89 / 124

页数：36

共 35 条

[11] Moderate deviations for empirical measures of Markov chains: Upper bounds
de Acosta, A
Chen, X
[J]. JOURNAL OF THEORETICAL PROBABILITY, 1998, 11 (04) : 1075 - 1110
[12] de Acosta A, 1997, ANN PROBAB, V25, P259
[13] LARGE DEVIATIONS FOR VECTOR-VALUED FUNCTIONALS OF A MARKOV-CHAIN - LOWER BOUNDS
DEACOSTA, A
[J]. ANNALS OF PROBABILITY, 1988, 16 (03) : 925 - 960
[14] Self-normalized moderate deviations and lils
Dembo, A
Shao, QM
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1998, 75 (01) : 51 - 65
[15] Dembo A., 1993, Large deviations techniques and applications
[16] Moderate deviations for Markov chains with atom
Djellout, H
Guillin, A
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2001, 95 (02) : 203 - 217
[17] Djellout H., 1999, STAT INFER STOCH PRO, V2, P195, DOI DOI 10.1023/A:1009950229386
[18] Duflo M., 1997, RANDOM ITERATIVE MOD
[19] Erdos P., 1960, Acta Math. Acad. Sci. Hung, V11, P137, DOI [DOI 10.1007/BF02020631, 10.1007/BF02020631]
[20] Large and moderate deviations for the local time of a recurrent Markov chain on Z2
Gantert, N
Zeitouni, O
[J]. ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 1998, 34 (05): : 687 - 704

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