Strong law of large numbers and Shannon-McMillan theorem for Markov chains field on Cayley tree

被引：5
|
作者：
Yang, WG
Liu, W
机构：
[1] Jiangsu Univ Sci & Technol, Fac Sci, Zhenjiang 212013, Peoples R China
[2] Hebei Univ Technol, Tianjin 300130, Peoples R China
来源：
ACTA MATHEMATICA SCIENTIA | 2001年 / 21卷 / 04期
关键词：
Cayley tree; random field; Markov chains field; strong law of large numbers; Shannon-McMillan theorem;
D O I：
10.1016/S0252-9602(17)30438-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper studies the strong law of large numbers and the Shannom-McMillan theorem for Markov chains field on Cayley tree. The authors first prove the strong law of large number on the frequencies of states and orderd couples of states for Markov chains field on Cayley tree. Then they prove the Shannon-McMillan theorem with a.e. convergence for Markov chains field on Cayley tree. In the proof, a new technique in the study the strong limit theorem in probability theory is applied.
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页码：495 / 502
页数：8
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