The law of the iterated logarithm for additive functionals of Markov chains

被引：4

作者：

Miao, Yu ^{[1
]}

Yang, Guangyu ^{[2
]}

机构：

[1] Henan Normal Univ, Coll Math & Informat Sci, Henan 453007, Peoples R China

[2] Zhengzhou Univ, Dept Math, Zhengzhou 450052, Peoples R China

来源：

STATISTICS & PROBABILITY LETTERS | 2008年 / 78卷 / 03期

关键词：

Markov chains; the law of the iterated logarithm; additive functionals; Dunford-Schwartz operator; shift processes;

D O I：

10.1016/j.spl.2007.05.032

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 paper, the law of the iterated logarithm for additive functionals of Markov chains is obtained under some weak conditions, which are weaker than the conditions of invariance principle of additive functionals of Markov chains in Maxwell and Woodroofe [2000. Central limit theorems for additive functionals of Markov chains. Ann. Probab. 28(2), 713-7241. (c) 2007 Elsevier B.V. All rights reserved.

引用

页码：265 / 270

页数：6

共 50 条

[1] An invariance principle for the law of the iterated logarithm for vector-valued additive functionals of Markov chains
Yang, Guangyu
Miao, Yu
Zhang, Xiaocai
[J]. MATHEMATICAL COMMUNICATIONS, 2013, 18 (01) : 79 - 86
[2] The law of iterated logarithm for additive functionals and martingale additive functionals of Harris recurrent Markov processes
Locherbach, Eva
Loukianova, Dasha
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2009, 119 (07) : 2312 - 2335
[3] Functional law of iterated logarithm for additive functionals of reversible Markov processes
Wu Liming
[J]. Acta Mathematicae Applicatae Sinica, 2000, 16 (2) : 149 - 161
[4] FUNCTIONAL LAW OF ITERATED LOGARITHM FOR ADDITIVE FUNCTIONALS OF REVERSIBLE MARKOV PROCESSES
吴黎明
[J]. Acta Mathematicae Applicatae Sinica, 2000, (02) : 149 - 161
[5] The Law of the Iterated Logarithm for Functionals of Harris Recurrent Markov Chains: Self Normalization
Xia Chen
[J]. Journal of Theoretical Probability, 1999, 12 : 421 - 445
[6] The law of the iterated logarithm for functionals of Harris recurrent Markov chains: Self normalization
Chen, X
[J]. JOURNAL OF THEORETICAL PROBABILITY, 1999, 12 (02) : 421 - 445
[7] An invariance principle for the law of the iterated logarithm for some Markov chains
Bolt, W.
Majewski, A. A.
Szarek, T.
[J]. STUDIA MATHEMATICA, 2012, 212 (01) : 41 - 53
[8] Empirical law of the iterated logarithm for Markov chains with a countable state space
Tsai, TH
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2000, 89 (02) : 175 - 191
[9] LAW OF ITERATED LOGARITHM FOR A CLASS OF NULL RECURRENT AND TRANSIENT MARKOV CHAINS
BREZIS, H
ROSENKRA.WA
SINGER, B
[J]. NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1971, 18 (01): : 229 - +
[10] LAW OF ITERATED LOGARITHM FOR A MARKOV PROCESS
PAKSHIRAJAN, RP
SREEHARI, M
[J]. ANNALS OF MATHEMATICAL STATISTICS, 1970, 41 (03): : 945 - +

← 1 2 3 4 5 →