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Quasi-Stationary Distributions

In: Constructive Computation in Stochastic Models with Applications

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  • Quan-Lin Li

    (Tsinghua University, Department of Industrial Engineering)

Abstract

In this chapter, we study quasi-stationary distributions for blockstructured Markov chains with either finitely-many levels or infinitely-many levels. We derive the RG-factorizations for the β -discounted block-structured transition matrix. We provide conditions for the state α -classification, and derive two sets of expressions for the quasi-stationary distribution. As important examples, we analyze Markov chains of M/G/1 type, Markov chains of GI/M/1 type, Markov chains of GI/G/1 type and level-dependent QBD processes.

Suggested Citation

  • Quan-Lin Li, 2010. "Quasi-Stationary Distributions," Springer Books, in: Constructive Computation in Stochastic Models with Applications, chapter 9, pages 432-525, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-11492-2_9
    DOI: 10.1007/978-3-642-11492-2_9
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