We consider a strictly substochastic matrix or a stochastic matrix with absorbing states. By using quasi-stationary distributions we show that there is an associated canonical Markov chain that is built from the resurrected chain, the absorbing states, and the hitting times, together with a random walk on the absorbing states, which is necessary for achieving time stationarity. Based upon the 2-stringing representation of the resurrected chain, we supply a stationary representation of the killed and the absorbed chains. The entropies of these representations have a clear meaning when one identifies the probability measure of natural factors. The balance between the entropies of these representations and the entropy of the canonical chain serves to check the correctness of the whole construction.

中文翻译：

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杀死复活的静止马尔可夫链的熵

我们考虑严格的亚随机矩阵或具有吸收状态的随机矩阵。通过使用准平稳分布，我们表明存在一个关联的规范马尔可夫链，该链由复活链、吸收状态和命中时间以及吸收状态上的随机游走构建而成，这是实现时间平稳性所必需的. 基于复活链的 2 弦表示，我们提供了被杀死和被吸收的链的固定表示。当识别自然因素的概率度量时，这些表示的熵具有明确的含义。这些表示的熵和规范链的熵之间的平衡用于检查整个构造的正确性。