Abstract:
We continue the work of improving the rate of convergence of ergodic homogeneous
Markov chains. The setting is more general than in previous papers: we are able to get rid
of the assumption about a common dominating measure and consider the case of inhomogeneous
Markov chains as well as more general state spaces. We give examples where the new bound
for the rate of convergence is the same as (resp. better than) the classical Markov–Dobrushin
inequality.
Keywords:
Markov chains, ergodicity, generalization of the Markov–Dobrushin condition, rate of convergence.
§§ 1–3 were written by the first author and § 4
by the second. §§ 1 and 2 were prepared within the framework of the
Fundamental Research Programme of the National Research University
‘Higher school of economics’ (NRU HSE). § 3 was supported by the Russian
Foundation for Basic Research, grant no. 20-01-00575a. Part of the research in § 4 was carried out
using the computational resources of the HPC facilities of NRU HSE.
Citation:
A. Yu. Veretennikov, M. A. Veretennikova, “On improved bounds and conditions for the convergence of Markov chains”, Izv. Math., 86:1 (2022), 92–125
\Bibitem{VerVer22}
\by A.~Yu.~Veretennikov, M.~A.~Veretennikova
\paper On improved bounds and conditions for the convergence of~Markov chains
\jour Izv. Math.
\yr 2022
\vol 86
\issue 1
\pages 92--125
\mathnet{http://mi.mathnet.ru/eng/im9076}
\crossref{https://doi.org/10.1070/IM9076}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4461227}
\zmath{https://zbmath.org/?q=an:1487.60130}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2022IzMat..86...92V}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000772181500001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85128180313}
Linking options:
https://www.mathnet.ru/eng/im9076
https://doi.org/10.1070/IM9076
https://www.mathnet.ru/eng/im/v86/i1/p98
This publication is cited in the following 4 articles:
A.A. Shchegolev, A.Yu. Veretennikov, “On Convergence Rate Bounds for a Class of Nonlinear Markov Chains”, Markov Processes And Related Fields, 2024, no. 2023 №5 (29), 619
A. Yu. Veretennikov, Springer INdAM Series, 56, Kolmogorov Operators and Their Applications, 2024, 315
“Abstracts of talks given at the 8th International Conference on Stochastic Methods”, Theory Probab. Appl., 68:4 (2024), 674–711
Y. Liu, Z. Wang, X. Lin, “Non-zero sum Nash game for discrete-time infinite Markov jump stochastic systems with applications”, Axioms, 12:9 (2023), 882
Citation in format AMSBIB
Contact us: