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In this chapter, we simplify the R-, U- and G-measures and the RG-factorizations for Markov chains of GI/G/1 type. Also, we derive a new RG-factorization for the repeated blocks and the four basic inequalities for the boundary blocks, which are useful in spectral analysis of Markov chains of GI/G/1 type. We analyze the dual Markov chain of any irreducible blockstructured Markov chain, and specifically...
In this chapter, we provide the UL- and LU-types of RG-factorizations for the transition probability mass matrix of any irreducible Markov renewal process in terms of the censoring technique. Specifically, we deal with Markov renewal processes of GI/G/1 type, including the RG-factorization, the RG-factorization for the repeated blocks, the spectral analysis and the first passage time.
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