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December, 1976 Noninvariance of $\bar d$-Convergence of $k$-Step Markov Approximations
Gideon Schwarz
Ann. Probab. 4(6): 1033-1035 (December, 1976). DOI: 10.1214/aop/1176995950

Abstract

Among the class of totally ergodic stationary discrete stochastic processes, the Bernoulli processes are characterized by $\bar{d}$-convergence of their canonical $k$-step Markov approximations. Here this property is shown to be no longer invariant under isomorphism if we leave the totally ergodic class. On the other hand, the isomorphism class of all Markov chains is shown to be not closed under $\bar{d}$-convergence.

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Gideon Schwarz. "Noninvariance of $\bar d$-Convergence of $k$-Step Markov Approximations." Ann. Probab. 4 (6) 1033 - 1035, December, 1976. https://doi.org/10.1214/aop/1176995950

Information

Published: December, 1976
First available in Project Euclid: 19 April 2007

zbMATH: 0366.60047
MathSciNet: MR425078
Digital Object Identifier: 10.1214/aop/1176995950

Subjects:
Primary: 60G10
Secondary: 28A65, 47A35

Rights: Copyright © 1976 Institute of Mathematical Statistics

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Vol.4 • No. 6 • December, 1976
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