Characterization of the conditional stationary distribution in Markov chains via systems of linear inequalities
Characterization of the conditional stationary distribution in Markov chains via systems of linear inequalities
复制标题
通过线性不等式系统表征马尔可夫链中的条件平稳分布
DOI：
10.1017/apr.2020.40
复制
发表时间：
2020
影响因子：
1.2
通讯作者：
Masatoshi Kimura and Tetsuya Takine
中科院分区：
文献类型：
--
作者：
車塚 彩菜;矢島 萌子;三好 直人;三好 直人;三好 直人;豊泉 洋，三好 直人;T. Takine;Masatoshi Kimura and Tetsuya Takine;Masatoshi Kimura and Tetsuya Takine
本文考虑上的遍历连续时间马氏链。对于任意固定的马氏链，我们研究了它的条件平稳分布。我们首先通过线性不等式组来刻画，并通过检查无穷小生成器的西北角块和其成员可从中的至少一个状态直接到达的第一状态的子集来识别包含的简化。这些结果与增广截断近似(ATA)密切相关，并为ATA提供了一些实际意义。接下来，我们考虑上述结果的扩展，使用的()西北角块和其成员可从中的至少一个州直接到达的第一个州的子集。此外，我们还引入了一种新的状态转移结构，称为(K，N)-无跳集，利用它我们得到了包含的最小凸多面体。
This paper considers ergodic, continuous-time Markov chains on . For an arbitrarily fixed , we study the conditional stationary distribution given the Markov chain being in . We first characterize via systems of linear inequalities and identify simplices that contain , by examining the northwest corner block of the infinitesimal generator and the subset of the first states whose members are directly reachable from at least one state in . These results are closely related to the augmented truncation approximation (ATA), and we provide some practical implications for the ATA. Next we consider an extension of the above results, using the ( ) northwest corner block of and the subset of the first states whose members are directly reachable from at least one state in . Furthermore, we introduce new state transition structures called (K, N)-skip-free sets, using which we obtain the minimum convex polytope that contains .