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Teor. Veroyatnost. i Primenen., 2005, Volume 50, Issue 2, Pages 371–379 (Mi tvp114)  

This article is cited in 14 scientific papers (total in 14 papers)

Short Communications

Estimates of stability for finite homogeneous continuous-time Markov chains

A. Yu. Mitrofanov

Saratov State University named after N. G. Chernyshevsky

Abstract: This paper obtains new stability estimates on infinite time interval and limit stability estimates for a finite homogeneous continuous-time Markov chain with a unique stationary distribution. The connection between the stability of the Markov chain under perturbation of the generator and the rate of convergence to stationarity is considered. Markov chains with a strongly accessible state are given special attention.

Keywords: continuous-time Markov chain, stability estimates under perturbations, ergodicity coefficient, exponential convergence, spectral gap, strongly accessible state.

DOI: https://doi.org/10.4213/tvp114

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English version:
Theory of Probability and its Applications, 2006, 50:2, 319–326

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Received: 13.11.2001
Revised: 07.10.2004

Citation: A. Yu. Mitrofanov, “Estimates of stability for finite homogeneous continuous-time Markov chains”, Teor. Veroyatnost. i Primenen., 50:2 (2005), 371–379; Theory Probab. Appl., 50:2 (2006), 319–326

Citation in format AMSBIB
\by A.~Yu.~Mitrofanov
\paper Estimates of stability for finite homogeneous continuous-time Markov chains
\jour Teor. Veroyatnost. i Primenen.
\yr 2005
\vol 50
\issue 2
\pages 371--379
\jour Theory Probab. Appl.
\yr 2006
\vol 50
\issue 2
\pages 319--326

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    This publication is cited in the following articles:
    1. Mukhamedov F. Al-Rawashdeh A., “Generalized Dobrushin Ergodicity Coefficient and Uniform Ergodicities of Markov Operators”, Positivity  crossref  mathscinet  isi
    2. Mitrophanov A.Yu., Lomsadze A., Borodovsky M., “Sensitivity of hidden Markov models”, J. Appl. Probab., 42:3 (2005), 632–642  crossref  mathscinet  zmath  isi  elib  scopus
    3. Heidergott B., Hordijk A., Leder N., “Series expansions for continuous-time Markov processes”, Oper. Res., 58:3 (2010), 756–767  crossref  mathscinet  zmath  isi  elib  scopus
    4. Lekadir O., Aissani D., “Error bounds on practical approximation for two tandem queue with blocking and non-preemptive priority”, Comput. Math. Appl., 61:7 (2011), 1810–1822  crossref  mathscinet  zmath  isi  elib  scopus
    5. Liu Yu., “Perturbation Bounds for the Stationary Distributions of Markov Chains”, SIAM J. Matrix Anal. Appl., 33:4 (2012), 1057–1074  crossref  mathscinet  zmath  isi  elib  scopus
    6. Zeifman A., Korotysheva A., “Perturbation Bounds for M-T/M-T/N Queue with Catastrophes”, Stoch. Models, 28:1 (2012), 49–62  crossref  mathscinet  zmath  isi  elib  scopus
    7. A. I. Zeifman, V. Yu. Korolev, A. V. Korotysheva, S. Ya. Shorgin, “Obschie otsenki ustoichivosti dlya nestatsionarnykh markovskikh tsepei s nepreryvnym vremenem”, Inform. i ee primen., 8:1 (2014), 106–117  mathnet  crossref  elib
    8. Liu YuanYuan, “Perturbation Analysis For Continuous-Time Markov Chains”, Sci. China-Math., 58:12 (2015), 2633–2642  crossref  mathscinet  zmath  isi  scopus
    9. Constantino P.H., Vlysidis M., Smadbeck P., Kaznessis Y.N., “Modeling Stochasticity in Biochemical Reaction Networks”, J. Phys. D-Appl. Phys., 49:9 (2016), 093001  crossref  adsnasa  isi  scopus
    10. Silvestrov D. Silvestrov S., “Asymptotic Expansions For Stationary Distributions of Perturbed Semi-Markov Processes”, Engineering Mathematics II: Algebraic, Stochastic and Analysis Structures For Networks, Data Classification and Optimization, Springer Proceedings in Mathematics & Statistics, 179, ed. Silvestrov S. Rancic M., Springer International Publishing Ag, 2016, 151–222  crossref  mathscinet  zmath  isi  scopus
    11. Jiang Sh., Liu Yu., Tang Y., “A Unified Perturbation Analysis Framework For Countable Markov Chains”, Linear Alg. Appl., 529 (2017), 413–440  crossref  mathscinet  zmath  isi  scopus
    12. Erkursun-ozcan N. Mukhamedov F., “Stability Estimates of Markov Semigroups on Abstract States Spaces”, Mediterr. J. Math., 17:2 (2020), 44  crossref  mathscinet  isi
    13. Zeifman A., Korolev V., Satin Ya., “Two Approaches to the Construction of Perturbation Bounds For Continuous-Time Markov Chains”, Mathematics, 8:2 (2020), 253  crossref  mathscinet  isi
    14. Kaszas B. Haller G., “Universal Upper Estimate For Prediction Errors Under Moderate Model Uncertainty”, Chaos, 30:11 (2020), 113144  crossref  mathscinet  isi
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