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The Geometry of Finite Markov Chains

Published online by Cambridge University Press:  20 November 2018

N. Pullman
N. Pullman*
Affiliation:
McGill University
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The purpose of this paper is to present a geometric theorem which provides a proof of a fundamental theorem of finite Markov chains.

The theorem, stated in matrix theoretic terms, concerns the asymptotic behaviour of the powers of an n by n stochastic matrix, that is, a matrix of non-negative entries each of whose row sums is 1. The matrix might arise from a repeated physical process which goes from one of n possible states to another at each iteration and whose probability of going to a state depends only on the state it is in at present and not on its more distant history.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 8 , Issue 3 , April 1965 , pp. 345 - 358
Copyright
Copyright © Canadian Mathematical Society 1965

References

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