耦合，广义耦合和不变测度的唯一性

arXiv: Probability Pub Date : 2020-08-26 DOI:10.1214/20-ecp363

M. Scheutzow

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引用次数: 3

摘要

给出了广义耦合下马尔可夫核不变概率测度的唯一性的充分条件。我们的主要定理推广了之前的结果，这些结果要求状态空间是波兰的。我们提供了一个例子，表明如果状态空间是可分离的和度量的(但不是波兰)，即使通过连续和正定函数定义的耦合存在，唯一性也可能失效。

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Couplings, generalized couplings and uniqueness of invariant measures

We provide sufficient conditions for uniqueness of an invariant probability measure of a Markov kernel in terms of (generalized) couplings. Our main theorem generalizes previous results which require the state space to be Polish. We provide an example showing that uniqueness can fail if the state space is separable and metric (but not Polish) even though a coupling defined via a continuous and positive definite function exists.

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arXiv: Probability

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