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Markov Chains in Many Dimensions
Dimitris N. Politis
Advances in Applied Probability
Vol. 26, No. 3 (Sep., 1994), pp. 756-774
Published by: Applied Probability Trust
Stable URL: http://www.jstor.org/stable/1427819
Page Count: 19
You can always find the topics here!Topics: Markov chains, Entropy, Chain rule, Random variables, Cubes, Mathematical sequences, Neighborhoods, Markov models, Modeling, Coordinate systems
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A generalization of the notion of a stationary Markov chain in more than one dimension is proposed, and is found to be a special class of homogeneous Markov random fields. Stationary Markov chains in many dimensions are shown to possess a maximum entropy property, analogous to the corresponding property for Markov chains in one dimension. In addition, a representation of Markov chains in many dimensions is provided, together with a method for their generation that converges to their stationary distribution.
Advances in Applied Probability © 1994 Applied Probability Trust