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Perturbation of the stationary distribution measured by ergodicity coefficients

Published online by Cambridge University Press:  01 July 2016

E. Seneta*
Affiliation:
University of Sydney
*
Postal address: Department of Mathematical Statistics, University of Sydney, NSW 2006 Australia.
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Abstract

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It is shown that an easily calculated ergodicity coefficient of a stochastic matrix P with a unique stationary distribution πT, may be used to assess sensitivity of πT to perturbation of P.

Type
Letters to the Editor
Copyright
Copyright © Applied Probability Trust 1988 

References

[1] Funderlic, R. E. and Meyer, C. D. (1986) Sensitivity of the stationary distribution vector for an ergodic Markov chain. Linear Algebra Appl. 76, 117.CrossRefGoogle Scholar
[2] Schweitzer, P. J. (1968) Perturbation theory and finite Markov chains. J. Appl. Prob. 5, 401413.Google Scholar
[3] Schweitzer, P. J. (1986) Posterior bounds on the equilibrium distribution of a finite Markov chain. Commun. Statist.-Stochastic Models 2, 323338.Google Scholar
[4] Seneta, E. (1981) Non-Negative Matrices and Markov Chains, 2nd edn. Springer-Verlag, New York.Google Scholar
[5] Seneta, E. (1987) Sensitivity to perturbation of the stationary distribution: some refinements (submitted).Google Scholar
[6] Tan, C. P. (1982) A functional form for a particular coefficient of ergodicity. J. Appl. Prob. 19, 858863.Google Scholar
[7] Tan, C. P. (1983) Coefficients of ergodicity with respect to vector norms. J. Appl. Prob. 20, 277287.Google Scholar