The group inverse of finite homogeneous QBD processes
Ana da Silva Soares, Guy Latouche · Stochastic Models · 2002
Generalized inverses of I−P, where P is a stochastic matrix, play an important role in the theory of Markov chains. In particular, the group inverse (I−P)# has a probabilistic interpretation and is well suited for algorithmic implementation. We determine (I−P)# for finite homogeneous quasi-birth-and-death (QBD) processes by exploiting both the structure of the process and the probabilistic properties of the group inverse.