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Northwest corner and banded matrix approximations to a Markov chain

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  • Yiqiang Q. Zhao
  • W. John Braun
  • Wei Li

Abstract

In this paper, we consider approximations to discrete time Markov chains with countably infinite state spaces. We provide a simple, direct proof for the convergence of certain probabilistic quantities when one uses a northwest corner or a banded matrix approximation to the original probability transition matrix. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 187–197, 1999

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  • Yiqiang Q. Zhao & W. John Braun & Wei Li, 1999. "Northwest corner and banded matrix approximations to a Markov chain," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(2), pages 187-197, March.
    • Handle: RePEc:wly:navres:v:46:y:1999:i:2:p:187-197
    DOI: 10.1002/(SICI)1520-6750(199903)46:23.0.CO;2-V
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    References listed on IDEAS

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    1. Gibson, Diana & Seneta, E., 1987. "Monotone infinite stochastic matrices and their augmented truncations," Stochastic Processes and their Applications, Elsevier, vol. 24(2), pages 287-292, May.
    2. Theodore J. Sheskin, 1985. "Technical Note—A Markov Chain Partitioning Algorithm for Computing Steady State Probabilities," Operations Research, INFORMS, vol. 33(1), pages 228-235, February.
    3. Winfried K. Grassmann & Daniel P. Heyman, 1993. "Computation of Steady-State Probabilities for Infinite-State Markov Chains with Repeating Rows," INFORMS Journal on Computing, INFORMS, vol. 5(3), pages 292-303, August.
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    5. Winfried K. Grassmann & Michael I. Taksar & Daniel P. Heyman, 1985. "Regenerative Analysis and Steady State Distributions for Markov Chains," Operations Research, INFORMS, vol. 33(5), pages 1107-1116, October.
    6. Edward P. C. Kao, 1991. "Using State Reduction for Computing Steady State Probabilities of Queues of GI/PH/1 Types," INFORMS Journal on Computing, INFORMS, vol. 3(3), pages 231-240, August.
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    Cited by:

    1. Yiqiang Q. Zhao & Wei Li & W. John Braun, 2003. "Censoring, Factorizations, and Spectral Analysis for Transition Matrices with Block-Repeating Entries," Methodology and Computing in Applied Probability, Springer, vol. 5(1), pages 35-58, March.

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