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Censoring, Factorizations, and Spectral Analysis for Transition Matrices with Block-Repeating Entries

Author

Listed:
  • Yiqiang Q. Zhao,

    () (School of Mathematics and Statistics, Carleton University)

  • Wei Li

    () (Department of Electical and Computer Engineering, University of Louisiana at Lafayette)

  • W. John Braun

    () (Department of Statistical and Actuarial Sciences, University of Western Ontario)

Abstract

In this paper, we use the Markov chain censoring technique to study infinite state Markov chains whose transition matrices possess block-repeating entries. We demonstrate that a number of important probabilistic measures are invariant under censoring. Informally speaking, these measures involve first passage times or expected numbers of visits to certain levels where other levels are taboo;they are closely related to the so-called fundamental matrix of the Markov chain which is also studied here. Factorization theorems for the characteristic equation of the blocks of the transition matrix are obtained. Necessary and sufficient conditions are derived for such a Markov chain to be positive recurrent, null recurrent, or transient based either on spectral analysis, or on a property of the fundamental matrix. Explicit expressions are obtained for key probabilistic measures, including the stationary probability vector and the fundamental matrix, which could be potentially used to develop various recursivealgorithms for computing these measures.

Suggested Citation

  • Yiqiang Q. Zhao, & Wei Li & W. John Braun, 2001. "Censoring, Factorizations, and Spectral Analysis for Transition Matrices with Block-Repeating Entries," RePAd Working Paper Series lrsp-TRS355, Département des sciences administratives, UQO.
  • Handle: RePEc:pqs:wpaper:0052005
    as

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    File URL: http://www.repad.org/ca/on/lrsp/TRS355.pdf
    File Function: First version, 2001
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    References listed on IDEAS

    as
    1. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
    2. Boyle, Phelim P., 1977. "Options: A Monte Carlo approach," Journal of Financial Economics, Elsevier, vol. 4(3), pages 323-338, May.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    block-Toeplitz transition matrices; factorization of characteristic functions; spectral analysis; fundamental matrix; conditions of recurrence and transience.;

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General

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