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 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 Teor. Veroyatnost. i Primenen., 1973, Volume 18, Issue 2, Pages 321–338 (Mi tvp4250)

Mixing Conditions for Markov Chains

Yu. A. Davydov

Abstract: In the paper, simple sufficient conditions are obtained for a homogeneous recurrent Markov chain with an arbitrary state space to possess the strong mixing property. These conditions enable constructing various examples of stationary processes with strong mixing property for which the central limit theorem fails to hold. For the examples constructed, the growth of the variance of partial sums and the decrease of the mixing coefficient are estimated.

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English version:
Theory of Probability and its Applications, 1973, 18:2, 312–328

Bibliographic databases:

Citation: Yu. A. Davydov, “Mixing Conditions for Markov Chains”, Teor. Veroyatnost. i Primenen., 18:2 (1973), 321–338; Theory Probab. Appl., 18:2 (1973), 312–328

Citation in format AMSBIB
\Bibitem{Dav73} \by Yu.~A.~Davydov \paper Mixing Conditions for Markov Chains \jour Teor. Veroyatnost. i Primenen. \yr 1973 \vol 18 \issue 2 \pages 321--338 \mathnet{http://mi.mathnet.ru/tvp4250} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=321183} \zmath{https://zbmath.org/?q=an:0297.60031} \transl \jour Theory Probab. Appl. \yr 1973 \vol 18 \issue 2 \pages 312--328 \crossref{https://doi.org/10.1137/1118033} 

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• http://mi.mathnet.ru/eng/tvp/v18/i2/p321

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. A. Yu. Veretennikov, “On rate of mixing and the averaging principle for hypoelliptic stochastic differential equations”, Math. USSR-Izv., 33:2 (1989), 221–231
2. S. A. Klokov, “On law bounds for mixing rates for a class of Markov processes”, Theory Probab. Appl., 51:3 (2007), 528–535
3. Sandric N., “Ergodicity of Lévy-Type Processes”, ESAIM-Prob. Stat., 20 (2016), 154–177
4. Rio E., “Asymptotic Theory of Weakly Dependent Random Processes”, Asymptotic Theory of Weakly Dependent Random Processes, Probability Theory and Stochastic Modelling, 80, Springer-Verlag Berlin, 2017, 1–204
5. Dedecker J., Gouezel S., Merlevede F., “Large and Moderate Deviations For Bounded Functions of Slowly Mixing Markov Chains”, Stoch. Dyn., 18:2 (2018), 1850017
6. Ibragimov I.A. Lifshits M.A. Nazarov A.I. Zaporozhets D.N., “On the History of St. Petersburg School of Probability and Mathematical Statistics: II. Random Processes and Dependent Variables”, Vestn. St Petersb. Univ.-Math., 51:3 (2018), 213–236