Distances between two-state Markov processes attainable by Markov joinings

Author:
Martin H. Ellis

Journal:
Trans. Amer. Math. Soc. **241** (1978), 129-153

MSC:
Primary 28A65

MathSciNet review:
0486409

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Abstract: The function which assigns to each pair of two-state Markov processes the set of partition distances between them attainable by a Markov process on their joint atoms is computed. It is found that the infimum of these distances, the ``Markov distance'' between the pair, fails to satisfy the Triangle Inequality, hence fails to be a metric; thus in some cases the -distance between two two-state Markov processes cannot be attained by a Markov process on their joint atoms.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1978-0486409-1

Keywords:
Stationary stochastic process,
Markov process,
joint process,
partition distance,
-distance,
Markov joining,
attaining ,
Markov joining attaining ,
distances attainable by Markov joinings

Article copyright:
© Copyright 1978
American Mathematical Society