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The Censored Markov Chain and the Best Augmentation

Y. Quennel Zhao and Danielle Liu
Journal of Applied Probability
Vol. 33, No. 3 (Sep., 1996), pp. 623-629
DOI: 10.2307/3215344
Stable URL: http://www.jstor.org/stable/3215344
Page Count: 7
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
The Censored Markov Chain and the Best Augmentation
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Abstract

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.

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