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Coefficients of Ergodicity: Structure and Applications
Advances in Applied Probability
Vol. 11, No. 3 (Sep., 1979), pp. 576-590
Published by: Applied Probability Trust
Stable URL: http://www.jstor.org/stable/1426955
Page Count: 15
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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: |λ|≤ τ (P), where λ is any non-unit eigenvalue of P. The essential purpose is exposition and unification, with the aid of simple informal proofs.
Advances in Applied Probability © 1979 Applied Probability Trust