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Izvestiya: Mathematics, 2022, Volume 86, Issue 1, Pages 92–125
DOI: https://doi.org/10.1070/IM9076 (Mi im9076) 		 
This article is cited in 3 scientific papers (total in 4 papers)

On improved bounds and conditions for the convergence of Markov chains

A. Yu. Veretennikovab, M. A. Veretennikovac

a Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
b National Research University "Higher School of Economics", Moscow
c The Zeeman Institute, University of Warwick, United Kingdom
English version PDF (644 kB) Citations (4)
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DOI: https://doi.org/10.1070/IM9076
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.
Funding agency Grant number
HSE Basic Research Program
Russian Foundation for Basic Research 20-01-00575a
§§ 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.
Received: 23.06.2020
Revised: 09.08.2020
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2022, Volume 86, Issue 1, Pages 98–133
DOI: https://doi.org/10.4213/im9076
Bibliographic databases:
Document Type: Article
UDC: 519.217.1+519.218.84
MSC: 60J05, 60J10, 37A25
Language: English
Original paper language: Russian
Citation: A. Yu. Veretennikov, M. A. Veretennikova, “On improved bounds and conditions for the convergence of Markov chains”, Izv. RAN. Ser. Mat., 86:1 (2022), 98–133; Izv. Math., 86:1 (2022), 92–125
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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