齐次树上三次循环树指标马氏链的强极限定理

潘恒;杨卫国

系统科学与数学 ›› 2010, Vol. 30 ›› Issue (5) : 710-720.

PDF(355 KB)
PDF(355 KB)
系统科学与数学 ›› 2010, Vol. 30 ›› Issue (5) : 710-720. DOI: 10.12341/jssms08988
论文

齐次树上三次循环树指标马氏链的强极限定理

    潘恒, 杨卫国
作者信息 +

Strong Limit Theorems for a Three Times Circulation Markov Chain Indexed by a Homogeneous Tree

    PAN Heng, YANG Weiguo
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摘要

首先给出齐次树上三次循环树指标马氏链的定义,利用构造鞅的方法,研究齐次树上三次循环树指标马氏链的强极限定理,并给出其状态及状态序偶发生频率的强大数定律.

Abstract

In this paper, the definition of a three times circulation Markov chain indexed by a homogeneous tree is introduced. Then strong limit theorems for a three times circulation Markon chain indexed by a homogeneous tree are given by using the method of construction martingle, and also the strong laws of large numbers for the frequencies of occurrence of states and ordered couple of states for this Markov chain are proven.

关键词

三次循环树 / 状态与状态序偶 / 强极限定理 / 强大数定律

Key words

Three times circulation Markov chain / states and ordered couples of states / strong limit theorems / strong laws of large numbers.

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潘恒 , 杨卫国. 齐次树上三次循环树指标马氏链的强极限定理. 系统科学与数学, 2010, 30(5): 710-720. https://doi.org/10.12341/jssms08988
PAN Heng , YANG Weiguo. Strong Limit Theorems for a Three Times Circulation Markov Chain Indexed by a Homogeneous Tree. Journal of Systems Science and Mathematical Sciences, 2010, 30(5): 710-720 https://doi.org/10.12341/jssms08988
中图分类号: 60F15    60J10   
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