Generalized inverses of Markovian kernels in terms of properties of the Markov chain

被引:18
作者
Hunter, Jeffrey J. [1 ]
机构
[1] Auckland Univ Technol, Sch Comp & Math Sci, Auckland 1142, New Zealand
关键词
Markov chains; Stochastic matrices; Stationary distributions; Moments of first passage times; Generalized matrix inverses; Group inverse; Fundamental matrix; Moore-Penrose generalized inverse; STATIONARY DISTRIBUTION; PERTURBATION BOUNDS; MIXING TIMES;
D O I
10.1016/j.laa.2013.08.037
中图分类号
O29 [应用数学];
学科分类号
070104 ;
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. (C) 2013 Elsevier Inc. All rights reserved.
引用
收藏
页码:38 / 55
页数:18
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