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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Markov process representations of general stochastic processes


Author: Dudley Paul Johnson
Journal: Proc. Amer. Math. Soc. 24 (1970), 735-738
MSC: Primary 60.62
DOI: https://doi.org/10.1090/S0002-9939-1970-0261690-0
MathSciNet review: 0261690
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Abstract: In this paper we show that any separable stochastic process on a compact metric space can be derived from a temporally homogeneous Markov process on the extreme points of a compact convex set of measures.


References [Enhancements On Off] (What's this?)

  • [1] Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, With the assistance of W. G. Bade and R. G. Bartle. Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers, Ltd., London, 1958. MR 0117523
  • [2] Paul-A. Meyer, Probability and potentials, Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London, 1966. MR 0205288

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0261690-0
Keywords: Stochastic process, temporally homogeneous Markov process, extreme points, Choquet's Theorem
Article copyright: © Copyright 1970 American Mathematical Society