Consider an ergodic Markov chain on a countable state space for which the return times have exponential tails. We show that the stationary version of any such chain is a finitary factor of an independent and identically distributed (i.i.d.) process. A key step is to show that any stationary renewal process whose jump distribution has exponential tails and is not supported on a proper subgroup of ${\mathbb {Z}}$ is a finitary factor of an i.i.d. process.

中文翻译：

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具有指数返回时间的马尔可夫链是有限的

考虑一个可数状态空间上的遍历马尔可夫链，其返回时间具有指数尾。我们表明，任何此类链的固定版本都是独立同分布 (iid) 过程的有限因素。一个关键步骤是证明任何跳跃分布具有指数尾且不受适当子群支持的平稳更新过程${\mathbb {Z}}$是一个独立同分布过程的有限因素。