A subgeometric estimate of the stability for time-homogeneous Markov chains

Golomozyĭ, V.

doi:10.1090/S0094-9000-2010-00808-8

A subgeometric estimate of the stability for time-homogeneous Markov chains

Author: V. V. Golomozyĭ
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 81 (2010).
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

Abstract | References | Similar Articles | Additional Information

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 $\Vert\boldsymbol\cdot\Vert _v$ .

1. N. V. Kartashov, Strong stable Markov chains, VSP, Utrecht; TBiMC Scientific Publishers, Kiev, 1996. MR 1451375
2. 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, https://doi.org/10.3150/07-BEJ5162
3. 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
4. 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, https://doi.org/10.1214/105051604000000620
5. D. Revuz, Markov chains, 2nd ed., North-Holland Mathematical Library, vol. 11, North-Holland Publishing Co., Amsterdam, 1984. MR 758799
6. Torgny Lindvall, Lectures on the coupling method, Dover Publications, Inc., Mineola, NY, 2002. Corrected reprint of the 1992 original. MR 1924231

Similar Articles

Retrieve articles in Theory of Probability and Mathematical Statistics with MSC (2010): 60J05

Retrieve articles in all journals with MSC (2010): 60J05

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

DOI: https://doi.org/10.1090/S0094-9000-2010-00808-8
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