Block-Structured Markov Chains

Quan-Lin Li ()
Additional contact information
Quan-Lin Li: Tsinghua University, Department of Industrial Engineering

Chapter 2 in Constructive Computation in Stochastic Models with Applications, 2010, pp 72-130 from Springer

Abstract: 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.

Keywords: stochastic model; block-structured Markov chain; the censoring technique; R-measure; U-measure; G-measure; A-measure; B-measure; censoring invariance; Wiener-Hopf equation; RG-factorization; state classification; stationary probability vector; transient probability; the first passage time (search for similar items in EconPapers)
Date: 2010
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-11492-2_2

Ordering information: This item can be ordered from
http://www.springer.com/9783642114922

DOI: 10.1007/978-3-642-11492-2_2

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().