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Continuity properties of a factor of Markov chains

Published online by Cambridge University Press:  24 March 2016

Walter A. F. de Carvalho ,
Sandro Gallo  and
Nancy L. Garcia
Walter A. F. de Carvalho
Affiliation:
Alameda Pitangueiras, 231, Engenheiro Coelho, São Paulo, 13.165-000, Brazil. Email address: walter.carvalho@unasp.edu.br
Sandro Gallo
Affiliation:
Departamento de Estatística - UFSCar, Rodovia Washington Luís, s/n - Jardim Guanabara, São Carlos, São Paulo, 13565-905, Brazil. Email address: sandro.gallo@ufscar.br
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Abstract

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.

Keywords

Factor mapcontinuity ratechains of infinite order
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 1 , March 2016 , pp. 216 - 230
Copyright
Copyright © Applied Probability Trust 2016 

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