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Sensitivity of finite Markov chains under perturbation

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  • Seneta, E.

Abstract

Meyer (1992) has developed inequalities in terms of the non-unit eigenvalues [lambda]j, j = 2,...,n, of a stochastic matrix P containing a single irreducible set of states, for the condition number maxa#ij, where A# = {a#ij} is the group generalized inverse of A = I - P. In this note we derive, succinctly, analogous inequalities for the alternative condition number, the ergodicity coefficient [tau]1(A#), using the properties of ergodicity coefficients: (min1 - [lambda]j)-1

Suggested Citation

  • Seneta, E., 1993. "Sensitivity of finite Markov chains under perturbation," Statistics & Probability Letters, Elsevier, vol. 17(2), pages 163-168, May.
    • Handle: RePEc:eee:stapro:v:17:y:1993:i:2:p:163-168
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    Cited by:

    1. Cruz, Juan Alberto Rojas, 2020. "Sensitivity of the stationary distributions of denumerable Markov chains," Statistics & Probability Letters, Elsevier, vol. 166(C).
    2. Maria Gamboa & Maria Jesus Lopez-Herrero, 2020. "The Effect of Setting a Warning Vaccination Level on a Stochastic SIVS Model with Imperfect Vaccine," Mathematics, MDPI, vol. 8(7), pages 1-23, July.
    3. Peyman Khorsand & Alireza Soltani, 2017. "Optimal structure of metaplasticity for adaptive learning," PLOS Computational Biology, Public Library of Science, vol. 13(6), pages 1-22, June.
    4. P.-C.G. Vassiliou, 2021. "Non-Homogeneous Markov Set Systems," Mathematics, MDPI, vol. 9(5), pages 1-25, February.
    5. Eilon Solan & Nicolas Vieille, 2002. "Perturbed Markov Chains," Discussion Papers 1342, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    6. Vahid Moosavi & Giulio Isacchini, 2017. "A Markovian model of evolving world input-output network," PLOS ONE, Public Library of Science, vol. 12(10), pages 1-18, October.
    7. Vahid Moosavi & Giulio Isacchini, 2016. "A Markovian Model of the Evolving World Input-Output Network," Papers 1612.06186, arXiv.org, revised Sep 2017.

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