Censoring Technique in Studying Block-Structured Markov Chains

Abstract: Markov chains with block-structured transition matrices find many applications in various areas. Such Markov chains are characterized by partitioning the state space into subsets called levels, each level consisting of a number of stages. Examples include Markov chains of GI/M/1 type and M/G/1 type, and, more generally, Markov chains of Toeplitz type, or GI/G/1 type. In the analysis of such Markov chains, a number of properties and measures which relate to transitions among levels play a dominant role, while transitions between stages within the same level are less important. The censoring technique has been frequently used in the literature in study-ing these measures and properties. In this paper, we use this same technique to study block-structured Markov chains. New results and new proofs on factorizations and convergence of algorithms will be provided