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Decidability of α (pk) > 0 for some k

Published online by Cambridge University Press:  14 July 2016

Richard W. Madsen
Richard W. Madsen*
Affiliation:
University of Missouri-Columbia
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Abstract

Paz (1963), (1971) has shown that for an n × n stochastic matrix P the property that some power of P has a positive ergodic coefficient is decidable. In particular he shows that α (Pk) > 0 for some k, only if it is positive for k = ½n(n – 1). However he states that it is not known whether this bound is sharp. In this paper a sharp bound is given, namely k =½(n – 1)2 + ½ or ½(n − 1)2 + 1 depending on whether n is even or odd. The proof of this is based on some results from number theory.

Keywords

ERGODIC COEFFICIENTDECIDABILITYSTOCHASTIC MATRIXMARKOV CHAIN
Type
Research Papers
Information
Journal of Applied Probability , Volume 12 , Issue 2 , June 1975 , pp. 333 - 340
Copyright
Copyright © Applied Probability Trust 1975 

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