The censored Markov chain and the best augmentation

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 distrib...

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Bibliographic Details
Published in:Journal of applied probability 1996-09, Vol.33 (3), p.623-629
Main Authors: Zhao, Y. Quennel, Liu, Danielle
Format: Article
Language:English
Subjects:
Approximation
Censorship
Combinatorial probability
Ergodic theory
Error rates
Exact sciences and technology
Markov analysis
Markov chains
Markov processes
Mathematics
Methods
Probability
Probability and statistics
Probability theory and stochastic processes
Research Papers
Sciences and techniques of general use
Steepest descent method
Studies
Taboos
Theory
Transition probabilities
Truncation
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Summary: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.
ISSN:0021-9002
1475-6072
DOI:10.2307/3215344