实现无限阶二元链的序偶之间的$\bar{d}$ -距离的耦合的完美模拟
Perfect simulation of a coupling achieving the $\bar{d}$-distance between ordered pairs of binary chains of infinite order
摘要：
我们明确地构建了一个耦合实现Ornstein的$\bar{d}$ -距离之间的序偶的二进制链的无限顺序。我们的主要工具是一个表示的转移概率的耦合二元链的无限顺序作为一个可数的混合马尔可夫转移概率的增加顺序。在适当的链记忆损失条件下，这种表示意味着耦合链可以表示为二元有限随机符号串的iid序列的级联。完美的模拟算法是基于这样一个事实，即我们几乎可以确定原点左侧的第一个再生点。
英文摘要：
We explicitly construct a coupling attaining Ornstein's $\bar{d}$-distance between ordered pairs of binary chains of infinite order. Our main tool is a representation of the transition probabilities of the coupled bivariate chain of infinite order as a countable mixture of Markov transition probabilities of increasing order. Under suitable conditions on the loss of memory of the chains, this representation implies that the coupled chain can be represented as a concatenation of iid sequence of bivariate finite random strings of symbols. The perfect simulation algorithm is based on the fact that we can identify the first regeneration point to the left of the origin almost surely.
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