A subgeometric estimate of the stability for time-homogeneous Markov chains
Author:
V. V. Golomozyĭ
Translated by:
S. Kvasko
Journal:
Theor. Probability and Math. Statist. 81 (2010), 35-50
MSC (2010):
Primary 60J05
DOI:
https://doi.org/10.1090/S0094-9000-2010-00808-8
Published electronically:
January 18, 2011
MathSciNet review:
2667308
Full-text PDF Free Access
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Abstract: Estimates for the stability of time-homogeneous Markov chains are obtained with the help of the coupling method. The results are proved for both the uniform metric and $\|\boldsymbol \cdot \|_v$.
References
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- Randal Douc, Eric Moulines, and Philippe Soulier, Computable convergence rates for sub-geometric ergodic Markov chains, Bernoulli 13 (2007), no. 3, 831–848. MR 2348753, DOI https://doi.org/10.3150/07-BEJ5162
- S. P. Meyn and R. L. Tweedie, Markov chains and stochastic stability, Communications and Control Engineering Series, Springer-Verlag London, Ltd., London, 1993. MR 1287609
- R. Douc, E. Moulines, and Jeffrey S. Rosenthal, Quantitative bounds on convergence of time-inhomogeneous Markov chains, Ann. Appl. Probab. 14 (2004), no. 4, 1643–1665. MR 2099647, DOI https://doi.org/10.1214/105051604000000620
- D. Revuz, Markov chains, 2nd ed., North-Holland Mathematical Library, vol. 11, North-Holland Publishing Co., Amsterdam, 1984. MR 758799
- Torgny Lindvall, Lectures on the coupling method, Dover Publications, Inc., Mineola, NY, 2002. Corrected reprint of the 1992 original. MR 1924231
References
- N. V. Kartashov, Strong Stable Markov Chains, VSP/TViMS, Utrecht, the Netherlands/Kiev, Ukraine, 1996. MR 1451375 (99e:60150)
- R. Douc, E. Moulines, and P. Soulier, Computable convergence rates for subgeometrically ergodic Markov chains, Bernoulli 13 (2007), no. 3, 831–848. MR 2348753 (2008j:60172)
- S. P. Mayn and R. L. Tweedie, Markov Chains and Stochastic Stability, Springer-Verlag, London, 1993. MR 1287609 (95j:60103)
- R. Douc, E. Moulines, and J. Rosenthal, Quantitative bounds for geometric convergence rates of Markov chains, Ann. Appl. Probab. 14 (2004), no. 4, 1643–1665. MR 2099647 (2005i:60146)
- D. Revuz, Markov Chains, North-Holland and American Elsevier, Amsterdam–Oxford and New York, 1997. MR 758799 (86a:60097)
- T. Lindvall, Lectures on Coupling Method, Dover Publications Inc., Mineola, 2002. MR 1924231
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Additional Information
V. V. Golomozyĭ
Affiliation:
Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine
Email:
mailtower@gmail.com
Keywords:
Markov chain,
coupling method,
stability
Received by editor(s):
November 13, 2009
Published electronically:
January 18, 2011
Article copyright:
© Copyright 2010
American Mathematical Society
