Coefficients of ergodicity: structure and applications
- 1 March 1979
- journal article
- research article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 11 (03) , 576-590
- https://doi.org/10.1017/s000186780003281x
Abstract
The concept of ‘coefficient of ergodicity’, τ(P), for a finite stochastic matrixP, 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 ofP.The essential purpose is exposition and unification, with the aid of simple informal proofs.Keywords
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