Markov Chains with Hybrid Repeating Rows - Upper-Hessenberg, Quasi-Toeplitz Structure of the Block Transition Probability Matrix

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.