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Coefficients of ergodicity: structure and applications

Published online by Cambridge University Press:  01 July 2016

E. Seneta
E. Seneta*
Affiliation:
The Australian National University
*
∗Postal addresss: Department of Statistics, The Australian National University, S.G.S., P.O. Box 4, Canberra A.C.T. 2600, Australia.
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Abstract

The concept of ‘coefficient of ergodicity’, τ(P), for a finite stochastic matrix P, is developed from a standpoint more general and less standard than hitherto, albeit synthesized from ideas in existing literature. Several versions of such a coefficient are studied theoretically and by numerical examples, and usefulness in applications compared from viewpoints which include the degree to which extension to more general matrices is possible. Attention is given to the less familiar spectrum localization property: where λ is any non-unit eigenvalue of P. The essential purpose is exposition and unification, with the aid of simple informal proofs.

Keywords

FINITE STOCHASTIC MATRICESCOEFFICIENTS OF ERGODICITYNON-NEGATIVE MATRICESSPECTRUM LOCALIZATIONGENERALIZED SCRAMBLING MATRICES
Type
Research Article
Information
Advances in Applied Probability , Volume 11 , Issue 3 , September 1979 , pp. 576 - 590
Copyright
Copyright © Applied Probability Trust 1979 

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Footnotes

Invited paper presented to 8th Conference on Stochastic Processes and their Applications, Canberra, 6–10 July, 1978.

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