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Coefficients of ergodicity with respect to vector norms

Published online by Cambridge University Press:  14 July 2016

Choon-Peng Tan
Choon-Peng Tan*
Affiliation:
University of Malaya
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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

ERGODIC TRANSITION MATRIXlp NORMSPECTRUM LOCALIZATION PROPERTYSTATIONARY DISTRIBUTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 20 , Issue 2 , June 1983 , pp. 277 - 287
Copyright
Copyright © Applied Probability Trust 1983 

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References

Isaacson, D. and Luecke, G. R. (1978) Strongly ergodic Markov chains and rates of convergence using spectral conditions. Stoch. Proc. Appl. 7, 113–121.Google Scholar
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Seneta, E. (1981) Non-negative Matrices and Markov Chains. Springer-Verlag, New York.Google Scholar
Tan, C.-P. (1982) A functional form for a particular coefficient of ergodicity. J. Appl. Prob. 19, 858–863.Google Scholar