论文标题
马尔可夫链的一般性条件就不变的添加剂措施而言
Ergodicity conditions for general Markov chains in terms of invariant finitely additive measures
论文作者
论文摘要
我们认为在可测量的（相）空间中具有离散时间的马尔可夫链，并且时间均匀。马尔可夫链是由经典的过渡函数定义的，在操作员处理的框架内，该函数在可测量有限函数的Banach空间以及有限有限添加度度量的Banach空间中生成了一对线性马尔可夫操作员。事实证明，马尔可夫链的众所周知的多包蛋白条件$（d）$（quasi \ compactness）等同于条件$（*）$：马尔可夫操作员的所有有限添加性不变性的度量是可计算的。在某些假设下，证明条件$（d）$和$（*）$也等同于条件$（**）$：Markov操作员的一组有限添加性度量是有限的。给出了奇异定理。
We consider general Markov chains with discrete time in an arbitrary measurable (phase) space and homogeneous in time. Markov chains are defined by the classical transition function which within the framework of the operator treatment generates a conjugate pair of linear Markov operators in the Banach space of measurable bounded functions and in the Banach space of bounded finite additive measures. It is proved that the well-known Doeblin condition $ (D) $ of ergodicity (quasi\-compactness) of the Markov chain is equivalent to the condition $ (*) $: all finitely additive invariant measures of the Markov operator are countably additive i.e. there are no invariant purely finitely additive measures. Under some assumptions, it is proved that the conditions $ (D) $ and $ (*) $ are also equivalent to the condition $ (**) $: the set of invariant finitely additive measures of a Markov operator is finite-dimensional. Ergodic theorems are given.
