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.