Strong law of large numbers of the delayed sums for Markov Chains indexed by a Cayley tree |
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| Authors: | Pingping Zhong Weiguo Yang Jie Yang |
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| Institution: | 1. Faculty of Science, Jiangsu University, Zhenjiang, China;2. Jingjiang College of Jiangsu University, Jiangsu University, Zhenjiang, Chinazpp2008@126.com |
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| Abstract: | AbstractIn this paper, we will study the strong law of large numbers of the delayed sums for Markov chains indexed by a Cayley tree with countable state spaces. Firstly, we prove a strong limit theorem for the delayed sums of the bivariate functions for Markov chains indexed by a Cayley tree. Secondly, the strong law of large numbers for the frequencies of occurrence of states of the delayed sums is obtained. As a corollary, we obtain the strong law of large numbers for the frequencies of occurrence of states for countable Markov chains indexed by a Cayley tree. |
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| Keywords: | Cayley tree Markov chains strong law of large numbers delayed sums |
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