A Strong Limit Theorem for Functions of Two-Ordered Markov Chains Indexed by a Kind of Non-Homogenous Tree

2009 ◽  
Author(s):  
Shao-hua Jin ◽  
Jian-guo Lu ◽  
Nan Wang ◽  
Hui-hui Jiang
Keyword(s):  
Limit Theorem ◽  
Markov Chains ◽  
Strong Limit ◽  
Strong Limit Theorem

THE STRONG LIMIT THEOREM FOR RELATIVE ENTROPY DENSITY RATES BETWEEN TWO ASYMPTOTICALLY CIRCULAR MARKOV CHAINS

2018 ◽  
Vol 33 (2) ◽  
pp. 161-171
Author(s):  
Ying Tang ◽  
Weiguo Yang ◽  
Yue Zhang
Keyword(s):  
Limit Theorem ◽  
Markov Chains ◽  
Relative Entropy ◽  
Entropy Density ◽  
Strong Limit ◽  
Strong Limit Theorem

In this paper, we are going to study the strong limit theorem for the relative entropy density rates between two finite asymptotically circular Markov chains. Firstly, we prove some lammas on which the main result based. Then, we establish two strong limit theorem for non-homogeneous Markov chains. Finally, we obtain the main result of this paper. As corollaries, we get the strong limit theorem for the relative entropy density rates between two finite non-homogeneous Markov chains. We also prove that the relative entropy density rates between two finite non-homogeneous Markov chains are uniformly integrable under some conditions.

A representation for the limiting random variable of a branching process with infinite mean and some related problems

1978 ◽  
Vol 15 (02) ◽  
pp. 225-234 ◽  
Author(s):  
Harry Cohn ◽  
Anthony G. Pakes
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Convergence Rate ◽  
Branching Process ◽  
Extreme Value Distribution ◽  
Random Variable ◽  
Random Sum ◽  
Strong Limit ◽  
Strong Limit Theorem ◽  
Watson Process

It is known that for a Bienaymé– Galton–Watson process {Zn } whose mean m satisfies 1 < m < ∞, the limiting random variable in the strong limit theorem can be represented as a random sum of i.i.d. random variables and hence that convergence rate results follow from a random sum central limit theorem. This paper develops an analogous theory for the case m = ∞ which replaces ‘sum' by ‘maximum'. In particular we obtain convergence rate results involving a limiting extreme value distribution. An associated estimation problem is considered.

THE ASYMPTOTIC EQUIPARTITION PROPERTY FOR ASYMPTOTIC CIRCULAR MARKOV CHAINS

2010 ◽  
Vol 24 (2) ◽  
pp. 279-288 ◽  
Author(s):  
Pingping Zhong ◽  
Weiguo Yang ◽  
Peipei Liang
Keyword(s):  
Markov Chains ◽  
Law Of Large Numbers ◽  
Strong Limit ◽  
Strong Law ◽  
Asymptotic Equipartition Property ◽  
Large Numbers ◽  
Nonhomogeneous Markov Chains ◽  
Strong Limit Theorem ◽  
Definition Of ◽  
Bivariate Functions

In this article, we study the asymptotic equipartition property (AEP) for asymptotic circular Markov chains. First, the definition of an asymptotic circular Markov chain is introduced. Then by applying the limit property for the bivariate functions of nonhomogeneous Markov chains, the strong limit theorem on the frequencies of occurrence of states for asymptotic circular Markov chains is established. Next, the strong law of large numbers on the frequencies of occurrence of states for asymptotic circular Markov chains is obtained. Finally, we prove the AEP for asymptotic circular Markov chains.

scholarly journals A strong limit theorem on gambling systems

2003 ◽  
Vol 84 (2) ◽  
pp. 262-273 ◽  
Author(s):  
Wen Liu ◽  
Jinting Wang
Keyword(s):  
Limit Theorem ◽  
Strong Limit ◽  
Strong Limit Theorem
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