Abstract
We show how to construct a topological Markov map of the interval whose invariant probability measure is the stationary law of a given stochastic chain of infinite order. In particular we characterize the maps corresponding to stochastic chains with memory of variable length. The problem treated here is the converse of the classical construction of the Gibbs formalism for Markov expanding maps of the interval.
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Acknowledgements
This work is part of USP project MaCLinC, “Mathematics, computation, language and the brain”, USP/COFECUB project “Stochastic systems with interactions of variable range” and CNPq project 476501/2009-1. A.G. is partially supported by a CNPq fellowship (grant 305447/2008-4). P.C. thanks Numec-USP for its kind hospitality.
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Collet, P., Galves, A. Chains of Infinite Order, Chains with Memory of Variable Length, and Maps of the Interval. J Stat Phys 149, 73–85 (2012). https://doi.org/10.1007/s10955-012-0579-6
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DOI: https://doi.org/10.1007/s10955-012-0579-6