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Finitary coding for the one-dimensional \(T,T^{-1}\) process with drift. (English) Zbl 1053.60035
The paper deals with \(T,T^{-1}\) processes associated with arbitrary random walks on \(Z^d\). One shows that, for a simple random walk with positive drift in one dimension, there is a finitary isomorphism from a finite state i.d.d. process to the corresponding \(T,T^{-1}\) process. To this end, one constructs a suitable countable state Markov chain, and then one constructs a finitary isomorphism from this Markov chain.

MSC:
60G10 Stationary stochastic processes
28C99 Set functions and measures on spaces with additional structure
37A35 Entropy and other invariants, isomorphism, classification in ergodic theory
37A50 Dynamical systems and their relations with probability theory and stochastic processes
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References:
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