A geometric proof of Markov ergodic theorem
Author:
R. Z. Yeh
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
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Abstract | References | Similar Articles | Additional Information
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.
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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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Additional Information
Keywords:
Stochastic simplex,
Markov transformation,
sequence of convex sets,
permutation of vertices,
boundary,
interior,
fixed points,
cyclic points,
acyclic transformation,
irreducible transformation,
ergodic stability,
transition matrix,
hyperplane
Article copyright:
© Copyright 1970
American Mathematical Society