论文标题
马尔可夫连锁店的严格不可约性和偏斜产品的奇迹性
Strict irreducibility of Markov chains and ergodicity of skew products
论文作者
论文摘要
我们考虑了一个衡量转化的家族，该家族在共同的概率空间上起作用，并由固定的千古马尔可夫链随机选择。此设置定义了一个随机动力系统（RDS）的实例，该实例可以用步骤偏斜产品来描述。在许多情况下，希望知道家庭的渴望是否意味着偏斜产物的成真性。引入了马尔可夫内核的严格不可减至的概念，我们将表征马尔可夫链的类别，上述含义是正确的。因此，我们将Bufetov的足够条件扩展到有限状态马尔可夫链的情况下到一般状态空间，并表明实际上也是必要的。作为应用程序，我们获得了沿厄尔贡定理中限制的明确描述，以进行合适的随机转换类别。
We consider a family of measure preserving transformations, which act on a common probability space and are chosen at random by a stationary ergodic Markov chain. This setting defines an instance of a random dynamical system (RDS), which may be described in terms of a step skew product. In many contexts it is desirable to know whether ergodicity of the family implies ergodicity of the skew product. Introducing the notion of strict irreducibility for Markov kernels we shall characterize the class of Markov chains for which the aforementioned implication holds true. We thereby extend a sufficient condition of Bufetov for the case of finite state Markov chains to general state spaces and show that it is in fact also necessary. As an application we obtain an explicit description of the limit in ergodic theorems for a suitable class of random transformations.
