Coefficients of ergodicity with respect to vector norms
- 1 June 1983
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 20 (2) , 277-287
- https://doi.org/10.2307/3213801
Abstract
The stationary distribution may be used to estimate the rate of geometric convergence to ergodicity for a finite homogeneous ergodic Markov chain. This is done by invoking the spectrum localization property of a new class of ergodicity coefficients defined with respect to column vector norms for the transition matrix P. Explicit functional forms in terms of the entries of P are obtained for these coefficients with respect to the l∞ and l1, norms, and comparison in performance with various known coefficients is made with the aid of numerical examples.Keywords
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