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.

**[1]**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.**[2]**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****[3]**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.**[4]**R. Z. Yeh,*On the effect of an affine transformation on a certain -convex set*, (to appear).

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1970-0263166-3

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