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.
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收藏
页码：89 / 124
页数：36
相关论文
共 35 条
[11]   Moderate deviations for empirical measures of Markov chains: Upper bounds [J].
de Acosta, A ;
Chen, X .
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 [J].
DEACOSTA, A .
ANNALS OF PROBABILITY, 1988, 16 (03) :925-960
[14]   Self-normalized moderate deviations and lils [J].
Dembo, A ;
Shao, QM .
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 [J].
Djellout, H ;
Guillin, A .
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 [J].
Gantert, N ;
Zeitouni, O .
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 1998, 34 (05) :687-704
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