基于马尔可夫链性质的马尔可夫核广义逆
Generalized inverses of Markovian kernels in terms of properties of the Markov chain
摘要：
其中P是有限不可约马尔可夫链的转移阵，马尔可夫核I-P的所有单条件广义逆都可以用平稳概率和潜在马尔可夫链的平均首次通过时间唯一地确定.特殊的子族包括I-P的群逆、马尔可夫链的Kemeny和Snell基本矩阵以及Moore-Penrose g-逆。广义逆的某些子族的元素也可以重新表示，涉及递归时间变量的二阶矩。本文还讨论了Kemeny常数和马尔可夫链扰动的一些应用。
英文摘要：
All one-condition generalized inverses of the Markovian kernel I - P, where P is the transition matrix of a finite irreducible Markov chain, can be uniquely specified in terms of the stationary probabilities and the mean first passage times of the underlying Markov chain. Special sub-families include the group inverse of I - P, Kemeny and Snell's fundamental matrix of the Markov chain and the Moore-Penrose g-inverse. The elements of some sub-families of the generalized inverses can also be re-expressed involving the second moments of the recurrence time variables. Some applications to Kemeny's constant and perturbations of Markov chains are also considered.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
