Censoring Technique in Studying Block-Structured Markov Chains
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 studying 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.
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