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Markov Chains in Many Dimensions

Part of: Inference from stochastic processes

Published online by Cambridge University Press:  01 July 2016

Dimitris N. Politis
Dimitris N. Politis*
Affiliation:
Purdue University
*
* Postal address: Department of Statistics, Purdue University, W. Lafayette, IN 47907, USA.
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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

MARKOV RANDOM FIELDSMAXIMUM ENTROPYRANDOM FIELDSRANDOM SEQUENCES

MSC classification

Primary: 62M20: Prediction
Secondary: 62M10: Time series, auto-correlation, regression, etc.

Information

Type
General Applied Probability
Information
Advances in Applied Probability , Volume 26 , Issue 3 , September 1994 , pp. 756 - 774
Copyright
Copyright © Applied Probability Trust 1994 

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