The purpose of this paper is to establish some limit theorems of delayed averages for countable nonhomogeneous Markov chains. The definition of the generalized C-strong ergodicity and the generalized uniformly C-strong ergodicity for countable nonhomogeneous Markov chains is introduced first. Then a theorem about the generalized C-strong ergodicity and the generalized uniformly C-strong ergodicity for the nonhomogeneous Markov chains is established, and its applications to the information theory are given. Finally, the strong law of large numbers of delayed averages of bivariate functions for countable nonhomogeneous Markov chains is proved.

中文翻译：

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可数非齐次马尔可夫链的延迟平均的一些极限定理

本文的目的是为可数非齐次马尔可夫链建立一些延迟平均的极限定理。广义的定义C- 强遍历性和泛化一致C-首先介绍了可数非齐次马尔可夫链的强遍历性。然后是关于广义的定理C- 强遍历性和泛化一致C-建立了非齐次马尔可夫链的强遍历性，并给出了它在信息论中的应用。最后，证明了可数非齐次马尔可夫链的二元函数大量延迟平均的强定律。