R. Grigorchuk, R. Kogan, Ya. Vorobets, “On Mealy–Moore coding and images of Markov measures”, Tr. Mosk. Mat. Obs., 2021, Volume 82, Issue 1,Pages <nobr>105

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On Mealy–Moore coding and images of Markov measures

R. Grigorchuk, R. Kogan, Ya. Vorobets

Department of Mathematics Texas A&M University, College Station

Abstract: We study the images of the Markov measures under transformations generated by the Mealy automata. We find conditions under which the image measure is absolutely continuous or singular relative to the Markov measure. Also, we determine statistical properties of the image of a generic sequence.

Key words and phrases: Markov measure, Mealy automaton, Moore diagram, regular rooted tree endomorphism, activity growth, pushforward measure, asymptotic frequency.

UDC: 517.987

MSC: 37A50, 37B10

Received: 08.02.2021

Language: English