On g-measures in symbolic dynamics

Wolfgang Krieger*, Benjamin Weiss

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

Finitary Markov processes are described in G. Morvai and B. Weiss, Prediction for discrete time series, Probability Theory and Related Fields 132 (2005), 1-12. The transition functions of finitary Markov processes are residually locally constant g-functions that can be extended by continuity to their maximal domain of definition. The study of their associated symbolic dynamics leads one to the D-shifts as introduced in W. Krieger, On g-functions for subshifts, Institute of Mathematical Statistics Lecture Notes-Monograph Series, Vol. 48, Dynamics & Stochastics, arXiv:math. DS/0608259, (2006), 306-316, We study the phenomena that can arise in residually locally constant and locally constant maximally defined g-functions on D-shifts, Markov shifts and synchronizing systems with respect to future measures and g-measures

Original languageEnglish
Pages (from-to)1-27
Number of pages27
JournalIsrael Journal of Mathematics
Volume176
Issue number1
DOIs
StatePublished - Mar 2010

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