Infinite block-structured transition matrices and their properties
Infinite block-structured transition matrices and their properties
复制标题
无限块结构转移矩阵及其性质
DOI：
10.1239/aap/1035228074
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发表时间：
1998
影响因子：
1.2
通讯作者：
W. J. Braun
中科院分区：
文献类型：
--
作者：
Yiqiang Q. Zhao;W. Li;W. J. Braun
本文研究了具有无限状态块结构转移矩阵的马氏链，其状态根据块结构划分为不同的层次，以及各种相关的测度。粗略地说，这些措施涉及首次通过时间或预期访问某些级别而不影响其他级别的次数。它们在马尔可夫链的研究中是非常重要的，并且经常起着关键的作用。根据这些测度，得到了马尔可夫链是正常返的、常返的或瞬态的充要条件.对于一般的不可约马氏链以及转移矩阵具有某种分块结构的马氏链，得到了一些结果。我们还讨论了这些测度的特征方程的分解或因式分解。在标量的情况下，我们找到这些特征函数的零点，因此使用这些零点来表征马尔可夫链。文中给出了一些例子和说明.
In this paper, we study Markov chains with infinite state block-structured transition matrices, whose states are partitioned into levels according to the block structure, and various associated measures. Roughly speaking, these measures involve first passage times or expected numbers of visits to certain levels without hitting other levels. They are very important and often play a key role in the study of a Markov chain. Necessary and/or sufficient conditions are obtained for a Markov chain to be positive recurrent, recurrent, or transient in terms of these measures. Results are obtained for general irreducible Markov chains as well as those with transition matrices possessing some block structure. We also discuss the decomposition or the factorization of the characteristic equations of these measures. In the scalar case, we locate the zeros of these characteristic functions and therefore use these zeros to characterize a Markov chain. Examples and various remarks are given to illustrate some of the results.