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Block-Structured Markov Chains

In: Constructive Computation in Stochastic Models with Applications

Author

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  • Quan-Lin Li

    (Tsinghua University, Department of Industrial Engineering)

Abstract

In this chapter, the censoring technique is applied to be able to deal with any irreducible block-structured Markov chain, which is either discrete-time or continuous-time. The R-, U- and G-measures are iteratively defined from two different censored directions: UL-type and LU-type. An important censoring invariance for the R- and G-measures is obtained. Using the censoring invariance, the Wiener-Hopf equations are derived, and then the UL- and UL-types of RG-factorizations are given. The stationary probability vector is given an R-measure expression; while the transient probability can be computed by means of the R-, U- and G-measures. Finally, the A- and B-measures are proposed in order to discuss the state classification of the block-structured Markov chain.

Suggested Citation

  • Quan-Lin Li, 2010. "Block-Structured Markov Chains," Springer Books, in: Constructive Computation in Stochastic Models with Applications, chapter 2, pages 72-130, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-11492-2_2
    DOI: 10.1007/978-3-642-11492-2_2
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