Markov Chains in Many Dimensions
- 1 September 1994
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 26 (3) , 756-774
- https://doi.org/10.2307/1427819
Abstract
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.Keywords
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