MARKOV-CHAINS IN MANY DIMENSIONS

A generalization of the notion of a stationary Markov chain in more th an one dimension is proposed, and is found to be a special class of ho mogeneous Markov random fields. Stationary Markov chains in many dimen sions are shown to possess a maximum entropy property, analogous to th e corresponding property for Markov chains in one dimension. In additi on, a representation of Markov chains in many dimensions is provided, together with a method for their generation that converges to their st ationary distribution.