A Unified Stability Theory for Classical and Monotone Markov Chains
A Unified Stability Theory for Classical and Monotone Markov Chains
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经典单调马尔可夫链的统一稳定性理论
DOI：
10.1017/jpr.2019.2
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发表时间：
2019
影响因子：
1
通讯作者：
Takashi Kamihigashi and John Stachurski
中科院分区：
文献类型：
--
作者：
桑田学;草深美奈子;Takashi Kamihigashi and John Stachurski
在本文中，我们整合了两股文献的稳定性一般状态马尔可夫链：传统的，全变差为基础的结果和最近的秩序理论的结果。首先，我们介绍了一个完整的度量博雷尔概率测度的基础上'部分'随机优势。然后，我们表明，许多传统的结果框架中设置的总变差距离有自然的推广到偏序设置时，采用这种度量。
In this paper we integrate two strands of the literature on stability of general state Markov chains: conventional, total-variation-based results and more recent order-theoretic results. First we introduce a complete metric over Borel probability measures based on ‘partial’ stochastic dominance. We then show that many conventional results framed in the setting of total variation distance have natural generalizations to the partially ordered setting when this metric is adopted.