Chains of Infinite Order, Chains with Memory of Variable Length, and Maps of the Interval

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.

USP project MaCLinC

USP project MaCLinC

USP/COFECUB project Stochastic systems with interactions of variable range

USP/COFECUB project "Stochastic systems with interactions of variable range"

CNPq

CNPq [476501/2009-1, 305447/2008-4]