Markov chains with hybrid repeating rows - Upper-Hessenberg, quasi-Toeplitz structure of the block transition probability matrix

摘要

In this paper we consider discrete-time multidimensional Markov chains having a block transition probability matrix which is the sum of a matrix with repeating block rows and a matrix of upper-Hessenberg, quasi-Toeplitz structure. We derive sufficient conditions for the existence of the stationary distribution, and outline two algorithms for calculating the stationary distribution.