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Coding Ergodic Processes to Approximate Bernoulli Processes

Published online by Cambridge University Press:  20 November 2018

A. Del Junco
A. Del Junco*
Affiliation:
University of Toronto, Toronto, Ontario
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In [1] Ornstein defined a metric on processes which, for processes (P, τ) and (Q, σ) with equal numbers of atoms, measures how closely the motions of P and Q under r and a, respectively, imitate each other. If we think of (P, τ) and (Q, σ) as stationary stochastic processes, and we assume (P, τ) and (Q, σ) are ergodic, then ((P, τ)(Q, σ)) < α says that with probability one a printout from (P, r) can be changed on a set of integers with density less than a to obtain a printout from (Q, σ).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 1 , 01 February 1976 , pp. 135 - 140
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Ornstein, D. S., An application of ergodic theory to probability theory, Ann. Probability 1, (1973), 43–65.Google Scholar
2. Ornstein, D. S., Bernoulli shifts with the same entropy are isomorphic, Advances in Math. 4 (1970), 337–352.Google Scholar
3. Ornstein, D. S., Factors of Bernoulli shifts are Bernoulli shifts, Advances in Math. 5 (1970), 349–364.Google Scholar
4. Shields, P. C., The theory of Bernoulli shifts (The University of Chicago Press, 1973).Google Scholar
5. Smorodinsky, M., Ergodic theory, entropy, Springer Lecture Notes in Mathematics, No. 214 (1971).Google Scholar