Translator Disclaimer
October, 1981 A Geometric Representation of a Stochastic Matrix: Theorem and Conjecture
Joel E. Cohen
Ann. Probab. 9(5): 899-901 (October, 1981). DOI: 10.1214/aop/1176994319

Abstract

An irreducible stochastic matrix may be constructed by partitioning a line of unit length into a finite number of intervals, shifting the line to the right $(\mod 1)$ by a small amount, and defining transition probabilities in terms of the overlaps among the intervals before and after the shift. It is proved that every $2 \times 2$ irreducible stochastic matrix arises from this construction. Does every $n \times n$ irreducible stochastic matrix arise this way?

Citation

Download Citation

Joel E. Cohen. "A Geometric Representation of a Stochastic Matrix: Theorem and Conjecture." Ann. Probab. 9 (5) 899 - 901, October, 1981. https://doi.org/10.1214/aop/1176994319

Information

Published: October, 1981
First available in Project Euclid: 19 April 2007

zbMATH: 0469.15009
MathSciNet: MR628884
Digital Object Identifier: 10.1214/aop/1176994319

Subjects:
Primary: 15A51
Secondary: 28A65, 60J10

Rights: Copyright © 1981 Institute of Mathematical Statistics

JOURNAL ARTICLE
3 PAGES


SHARE
Vol.9 • No. 5 • October, 1981
Back to Top