Some limit theorems for the second-order Markov chains indexed by a general infinite tree with uniform bounded degree

被引：8

作者：

Shi, Zhiyan ^{[1
]}

Yang, Weiguo ^{[1
]}

Tian, Lixin ^{[1
]}

Zang, Qingpei ^{[1
,2
]}

机构：

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

[2] Huaiyin Normal Univ, Sch Math Sci, Huaian 223300, Peoples R China

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2012年

基金：

中国国家自然科学基金;

关键词：

uniformly bounded tree; second-order Markov chain; strong law of large numbers; Shannon-McMillan theorem; ASYMPTOTIC EQUIPARTITION PROPERTY; HOMOGENEOUS TREE; LARGE NUMBERS; STRONG LAW;

D O I：

10.1186/1029-242X-2012-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study a convergence theorem for a finite second-order Markov chain indexed by a general infinite tree with uniformly bounded degree. Meanwhile, the strong law of large numbers (LLN) and Shannon-McMillan theorem for a finite second-order Markov chain indexed by this tree are obtained. 2000 Mathematics Subject Classification: 60F15; 60J10.

引用

页数：10

共 29 条

[1] Some limit theorems for the second-order Markov chains indexed by a general infinite tree with uniform bounded degree
Zhiyan Shi
Weiguo Yang
Lixin Tian
Qingpei Zang
Journal of Inequalities and Applications, 2012
[2] Some Limit Theorems for Nonhomogeneous Markov Chains Indexed by an Infinite Tree with Uniformly Bounded Degree
Wang, Kangkang
THAI JOURNAL OF MATHEMATICS, 2012, 10 (02): : 233 - 243
[3] Some Limit Properties of Random Transition Probability for Second-Order Nonhomogeneous Markov Chains Indexed by a Tree
Zhiyan Shi
Weiguo Yang
Journal of Inequalities and Applications, 2009
[4] Some Limit Properties of Random Transition Probability for Second-Order Nonhomogeneous Markov Chains Indexed by a Tree
Shi, Zhiyan
Yang, Weiguo
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2009,
[5] Some Strong Limit Theorems for Markov Chains of Order Two Indexed by a Non-homogeneous Tree
Jin, Shaohua
Jiang, Huihui
Zhang, Lijuan
Zhong, Yanyan
PROCEEDINGS OF FIRST INTERNATIONAL CONFERENCE OF MODELLING AND SIMULATION, VOL II: MATHEMATICAL MODELLING, 2008, : 35 - 39
[6] Strong law of large numbers for Markov chains indexed by an infinite tree with uniformly bounded degree
HUANG HuiLin~1 YANG WeiGuo~(2+) 1 Department of Mathematics
2 Faculty of Science
Science in China(Series A:Mathematics), 2008, (02) : 195 - 202
[7] Strong law of large numbers for Markov chains indexed by an infinite tree with uniformly bounded degree
Huang HuiLin
Yang WeiGuo
SCIENCE IN CHINA SERIES A-MATHEMATICS, 2008, 51 (02): : 195 - 202
[8] Strong law of large numbers for Markov chains indexed by an infinite tree with uniformly bounded degree
HuiLin Huang
WeiGuo Yang
Science in China Series A: Mathematics, 2008, 51 : 195 - 202
[9] Strong Law of Large Numbers for Countable Markov Chains Indexed by an Infinite Tree with Uniformly Bounded Degree
Wang, Bao
Yang, Weiguo
Shi, Zhiyan
Zang, Qingpei
JOURNAL OF APPLIED MATHEMATICS, 2014,
[10] Some limit properties for Markov chains indexed by a homogeneous tree
Yang, WG
STATISTICS & PROBABILITY LETTERS, 2003, 65 (03) : 241 - 250

← 1 2 3 →