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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
Published by: Applied Probability Trust
Stable URL: http://www.jstor.org/stable/3215344
Page Count: 7
You can always find the topics here!Topics: Markov chains, Censorship, Transition probabilities, Approximation, Steepest descent method, Truncation, Matrices, Former slaves, Mathematical problems, Ergodic theory
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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.
Journal of Applied Probability © 1996 Applied Probability Trust