Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A geometric proof of Markov ergodic theorem
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by R. Z. Yeh
Proc. Amer. Math. Soc. 26 (1970), 335-340
DOI: https://doi.org/10.1090/S0002-9939-1970-0263166-3

Abstract:

A geometric approach combined with topological results leads to a criterion for ergodic stability of Markov transformations. The matrix representation of this criterion provides an alternative proof for the well-known theorem of Markov in probability.
References
    A. A. Markov, Investigation of a noteworthy case of dependent trials, Izv. Ros. Akad. Nauk 1 (1907) (Russian) or B. V. Gnedenko, Course in the theory of probability, Fizmatgiz, Moscow, 1961; English transl., Chelsea, New York, 1962, pp. 142-145. MR 25 #2622.
  • V. Borovikov, On the intersection of a sequence of simplexes, Uspehi Matem. Nauk (N.S.) 7 (1952), no. 6(52), 179–180 (Russian). MR 0053505
  • F. R. Gantmacher, The theory of matrices, GITTL, Moscow, 1953; English transl., Vol. 2, Chelsea, New York, 1959, pp. 50-93. MR 16, 438; MR 21 #6372c. R. Z. Yeh, On the effect of an affine transformation on a certain $k$-convex set, (to appear).
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Bibliographic Information
  • © Copyright 1970 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 26 (1970), 335-340
  • MSC: Primary 60.65
  • DOI: https://doi.org/10.1090/S0002-9939-1970-0263166-3
  • MathSciNet review: 0263166