论文标题
普遍的多布鲁刺激性系数和非殖民马尔可夫连锁店
Generalized Dobrushin Ergodicity Coefficient and Ergodicities of Non-homogeneous Markov Chains
论文作者
论文摘要
在我们之前的论文中，已经引入并研究了马尔可夫操作员（在抽象状态空间上作用于抽象状态空间）的广义涂布金奇迹系数。事实证明，引入的系数比通常的登山系数更有效。在目前的工作中，通过左侧一致的马尔可夫预测和普遍的多布鲁什的奇迹系数，我们研究了抽象状态空间上非均匀离散分离马尔可夫链（NDMC）的统一和弱$ $ p $ erer的。很容易表明统一的$ p $ ergodicity意味着一个弱的，但总的来说，相反的情况并非如此。因此，某些条件与NDMC的$ p $ ergodicity一起提供，这意味着其均匀的$ p $ erergodicity。此外，通过ndmc的$ $ p $ erergoditicity的状态发现了必要和充分的条件。 $ p $ er-officticity还通过扰动进行了研究。获得了几种扰动结果，使我们能够产生均匀和弱$ p $ ergogodic NDMC的非平凡示例。此外，还获得了一些类别的结果。我们强调，所有获得的结果在经典和非交通概率中都有潜在的应用。
In our earlier paper, a generalized Dobrushin ergodicity coefficient of Markov operators (acting on abstract state spaces) with respect to a projection $P$, has been introduced and studied. It turned out that the introduced coefficient was more effective than the usual ergodicity coefficient. In the present work, by means of a left consistent Markov projections and the generalized Dobrushin's ergodicity coefficient, we investigate uniform and weak $P$-ergodicities of non-homogeneous discrete Markov chains (NDMC) on abstract state spaces. It is easy to show that uniform $P$-ergodicity implies a weak one, but in general the reverse is not true. Therefore, some conditions are provided together with weak $P$-ergodicity of NDMC which imply its uniform $P$-ergodicity. Furthermore, necessary and sufficient conditions are found by means of the Doeblin's condition for the weak $P$-ergodicity of NDMC. The weak $P$-ergodicity is also investigated in terms of perturbations. Several perturbative results are obtained which allow us to produce nontrivial examples of uniform and weak $P$-ergodic NDMC. Moreover, some category results are also obtained. We stress that all obtained results have potential applications in the classical and non-commutative probabilities.
