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A functional form for a particular coefficient of ergodicity

Published online by Cambridge University Press:  14 July 2016

Choon-Peng Tan
Choon-Peng Tan*
Affiliation:
University of Malaya
*
∗ Postal address: Department of Mathematics, University of Malaya, Kuala Lumpur 22–11, Malaysia. The author is on sabbatical leave at the Department of Mathematical Statistics, Columbia University, NY 10027, U.S.A. during the 1982–83 academic year.
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Abstract

Seneta, in a recent paper, presented a general treatment of the concept of ‘coefficient of ergodicity', τ (P), for a finite stochastic matrix P. In this paper, a functional form for τ∞(P) in terms of the attributes of P is determined. It is shown that, by increasing the dimension of P, τ∞(Ρ) can assume any large value. In view of this, τ∞ will be practically useful only in the case τ∞(P) ≦ τ1(P), where τ1(P) is the well-known Dobrushin or delta coefficient.

Keywords

FINITE STOCHASTIC MATRIXFUNCTIONAL FORMGEOMETRIC CONVERGENCE RATE
Type
Short Communications
Information
Journal of Applied Probability , Volume 19 , Issue 4 , December 1982 , pp. 858 - 863
Copyright
Copyright © Applied Probability Trust 1982 

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References

Isaacson, D. L. and Madsen, R. W. (1976) Markov Chains. Wiley Interscience, New York.Google Scholar
Paz, A. (1971) Introduction to Probabilistic Automata. Academic Press, New York.Google Scholar
Seneta, E. (1979) Coefficients of ergodicity: structure and applications. Adv. Appl. Prob. 11, 576–590.CrossRefGoogle Scholar