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中文摘要：
引入了渐近循环马氏链的概念，它是循环马氏链概念的推广．首先研究了在强遍历的条件下，可列循环马氏链的收敛速度，作为主要结论给出了当满足不同条件时可列渐近循环马氏链的C-强遍历性，一致C-强遍历性和一致C-强遍历的收敛速度。
英文摘要：
In this paper, we introduce the definition of asymptotic circular Markov chains, it is an extension of the definition of circular Markov chains. In this paper fist studied the convergence rate of the countable circular Markov chains under the condition of strong ergodic. As main condusion; we discusses the C-strong ergodicity, the uniformly C-Strong ergodicity and the rate of convergence in ceasaro sense for countable asymptotic circular Markov chains under different conditions.
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