STRONG LAW OF LARGE NUMBERS FOR MARKOV CHAINS INDEXED BY SPHERICALLY SYMMETRIC TREES

被引：13

作者：

Peng Weicai ^{[1
]}

Yang Weiguo ^{[2
]}

Shi Zhiyan ^{[2
]}

机构：

[1] Chaohu Univ, Dept Math, Chaohu 238000, Peoples R China

[2] Jiangsu Univ, Fac Sci, Zhenjiang 212013, Peoples R China

来源：

PROBABILITY IN THE ENGINEERING AND INFORMATIONAL SCIENCES | 2015年 / 29卷 / 03期

基金：

美国国家科学基金会;

关键词：

HOMOGENEOUS TREE; FIELDS;

D O I：

10.1017/S0269964815000108

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this paper, we main consider spherically symmetric tree T. First, under the condition lim sup(n ->infinity) vertical bar T-(n)vertical bar/vertical bar L-n vertical bar < infinity, we investigate the strong law of large numbers (SLLNs) for T-indexed Markov chains on the nth level of T. Then, combining the Stolz theorem, we obtain the SLLNs on T. Finally, we get Shannon-McMillan theorem for T-indexed Markov chains. The obtained theorems are generalizations of some known results on Cayley tree T-C,T-N and Bethe tree T-B,T-N.

引用

页码：473 / 481

页数：9

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