数学物理学报(英文版)

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STRONG LAW OF LARGE NUMBERS AND ASYMPTOTIC EQUIPARTITION PROPERTY FOR NONSYMMETRIC MARKOV CHAIN FIELDS ON CAYLEY TREES

包振华; 叶中行   

  1. 辽宁师范大学数学学院, 大连 116029
  • 收稿日期:2005-09-28 修回日期:2006-01-10 出版日期:2007-10-20 发布日期:2007-10-20
  • 通讯作者: 包振华
  • 基金资助:

    Supported by National Basic Research Program of China (973 Program No.2007CB814903) and National Science Foundation of China (70671069)

STRONG LAW OF LARGE NUMBERS AND ASYMPTOTIC EQUIPARTITION PROPERTY FOR NONSYMMETRIC MARKOV CHAIN FIELDS ON CAYLEY TREES

Bao Zhenhua; Ye Zhongxing   

  1. School of Mathematics, Liaoning Normal University, Dalian 116029, China
  • Received:2005-09-28 Revised:2006-01-10 Online:2007-10-20 Published:2007-10-20
  • Contact: Bao Zhenhua

摘要:

Some strong laws of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields
(NSMC) on Cayley trees are studied. In the proof, a new technique for the study of strong limit theorems of Markov chains is extended to the case of Markov chain fields. The asymptotic equipartition properties with almost everywhere (a.e.) convergence for NSMC on Cayley trees are obtained.

关键词: Cayley tree, nonsymmetric Markov chain fields,
strong law of large numbers,
asymptotic equipartition property

Abstract:

Some strong laws of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields
(NSMC) on Cayley trees are studied. In the proof, a new technique for the study of strong limit theorems of Markov chains is extended to the case of Markov chain fields. The asymptotic equipartition properties with almost everywhere (a.e.) convergence for NSMC on Cayley trees are obtained.

Key words: Cayley tree, nonsymmetric Markov chain fields,
strong law of large numbers,
asymptotic equipartition property

中图分类号: 

  • 60J25