论文标题
马尔可夫链：有限加性措施和经典循环的循环
General Markov Chains: Cycles of Finitely Additive Measures and Classical Cycles of States
论文作者
论文摘要
在操作员处理的框架中考虑了任意相空间中的马尔可夫链。马尔可夫操作员从数量添加的措施的空间继续进行有限添加度量的空间。构建了由相应操作员产生的度量的循环，并引入了代数操作。获得的主要结果之一是，任何有限加性测量的循环都可以唯一地分解到坐标的坐标之和，这是一个可计数添加剂度量的循环和纯有限加性措施的循环。我们证明，我们已经在一致性的条件和结果上证明了与一般标准链的衡量标准的条件和后果。在某些条件下（在某些条件下）证明了一个定理，如果马尔可夫链的有限添加循环是唯一的，那么它是可添加的。
General Markov chains in an arbitrary phase space are considered in the framework of the operator treatment. Markov operators continue from the space of countably additive measures to the space of finitely additive measures. Cycles of measures generated by the corresponding operator are constructed, and algebraic operations on them are introduced. One of the main results obtained is that any cycle of finitely additive measures can be uniquely decomposed into the coordinate-wise sum of a cycle of countably additive measures and a cycle of purely finitely additive measures.We have proved theorems on the conditions and consequences of consistency cycles of measures with cycles of sets of states of General Markov chains. A theorem is proved (under certain conditions) that if a finitely additive cycle of a Markov chain is unique, then it is countably additive.
