Distances between twostate Markov processes attainable by Markov joinings
Author:
Martin H. Ellis
Journal:
Trans. Amer. Math. Soc. 241 (1978), 129153
MSC:
Primary 28A65
MathSciNet review:
0486409
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Abstract: The function which assigns to each pair of twostate 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 twostate Markov processes cannot be attained by a Markov process on their joint atoms.
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 T. Kamae, U. Krengel and G. L. O'Brien, Stochastic inequalities on partially ordered spaces, Ann. of Probability 5 (1977), 899912. MR 0494447 (58:13308)
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 J. G. Kemeny and J. L. Snell, Finite Markov chains, Van Nostrand, Princeton, N. J., 1960. MR 22 #5998. MR 0115196 (22:5998)
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 , Ergodic theory, randomness and dynamical systems, Yale Univ. Press, New Haven, Conn., 1974. MR 0447525 (56:5836)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197804864091
PII:
S 00029947(1978)04864091
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
