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引用次数: 0
摘要
我们研究了两种半群规律性之间的关系,即 e 特性和最终连续性,这两种特性都有助于波兰空间上马尔可夫过程的遍历性。更准确地说,我们证明了对于离散时间的马尔可夫-费勒半群和连续时间的随机连续马尔可夫-费勒半群,如果存在一个遍历度量,其支持有一个非空的内部,那么在支持的内部就满足 e-属性。特别是,这意味着在每个遍历度量的支持上,对于离散时间和随机连续连续时间的马尔可夫-费勒半群,e-属性和最终连续性是等价的。
Relation Between the Eventual Continuity and the E-property for Markov-Feller Semigroups
We investigate some relations between two kinds of semigroup regularities, namely the e-property and the eventual continuity, both of which contribute to the ergodicity for Markov processes on Polish spaces. More precisely, we prove that for Markov-Feller semigroup in discrete time and stochastically continuous Markov-Feller semigroup in continuous time, if there exists an ergodic measure whose support has a nonempty interior, then the e-property is satis ed on the interior of the support. In particular, it implies that, restricted on the support of each ergodic measure, the e-property and the eventual continuity are equivalent for the discrete-time and the stochastically continuous continuous-time Markov-Feller semigroups.
期刊介绍:
Acta Mathematicae Applicatae Sinica (English Series) is a quarterly journal established by the Chinese Mathematical Society. The journal publishes high quality research papers from all branches of applied mathematics, and particularly welcomes those from partial differential equations, computational mathematics, applied probability, mathematical finance, statistics, dynamical systems, optimization and management science.