Continuity properties of a factor of Markov chains

Walter A. F. de Carvalho, Sandro Gallo and Nancy L. Garcia

Starting from a Markov chain with a finite or a countable infinite alphabet, we consider the chain obtained when all but one symbol are indistinguishable for the practitioner. We study conditions on the transition matrix of the Markov chain ensuring that the image chain has continuous or discontinuous transition probabilities with respect to the past.

The whole paper is available here.

 

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