论文标题
马尔可夫链转换概率的收敛性
Convergence of Markov chain transition probabilities
论文作者
论文摘要
考虑一个具有相当一般状态空间的离散时间马尔可夫链，该链具有不变的概率度量$μ$。文献中有几种足够的条件可以保证全部或$μ$的收敛性 - 几乎所有过渡概率到$μ$的总变化（TV）度量标准：不可约性，繁殖性，过渡概率的等效性能或耦合属性。在这项工作中，我们以这样的方式审查并改善了其中的一些标准，使它们变得必要和足够，足以分别用于所有$μ$的电视收敛性 - 几乎所有过渡概率。此外，我们讨论了所谓的广义耦合。
Consider a discrete time Markov chain with rather general state space which has an invariant probability measure $μ$. There are several sufficient conditions in the literature which guarantee convergence of all or $μ$-almost all transition probabilities to $μ$ in the total variation (TV) metric: irreducibility plus aperiodicity, equivalence properties of transition probabilities, or coupling properties. In this work, we review and improve some of these criteria in such a way that they become necessary and sufficient for TV convergence of all respectively $μ$-almost all transition probabilities. In addition, we discuss so-called generalized couplings.
