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2 results

  • The censored Markov chain and the best augmentation

  • Part of
  • Y. Quennel Zhao, Danielle Liu
  • Journal:
    Journal of Applied Probability / Volume 33 / Issue 3 / September 1996
    Published online by Cambridge University Press:
    14 July 2016, pp. 623-629
    Print publication:
    September 1996

  • Computationally, when we solve for the stationary probabilities for a countable-state Markov chain, the transition probability matrix of the Markov chain has to be truncated, in some way, into a finite matrix. Different augmentation methods might be valid such that the stationary probability distribution for the truncated Markov chain approaches that for the countable Markov chain as the truncation size gets large. In this paper, we prove that the censored (watched) Markov chain provides the best approximation in the sense that, for a given truncation size, the sum of errors is the minimum and show, by examples, that the method of augmenting the last column only is not always the best.