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- W2094547532 abstract "Previous article Next article Mixing Conditions for Markov ChainsYu. A. DavydovYu. A. Davydovhttps://doi.org/10.1137/1118033PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] V. A. Volkonskii and , Yu. A. Rozanov, Some limit theorems for random functions. I, Theor. Probability Appl., 4 (1959), 178–197 10.1137/1104015 MR0121856 0092.33502 LinkGoogle Scholar[2] I. Gel'fand, , D. Raikov and , G. Shilov, Commutative normed rings, Translated from the Russian, with a supplementary chapter, Chelsea Publishing Co., New York, 1964, 306– MR0205105 Google Scholar[3] R. L. Dobrushin, Central limit theorem for non-stationary Markov chains, I, Theory Prob. Applications, 1 (1956), 65–80, II, 1 (1956), pp. 329–383 10.1137/1101006 LinkGoogle Scholar[4] Yu. A. Davydov, On the strong mixing property for Markov chains with a countable number of states, Soviet Mathematics, 10 (1969), 825–827 0191.47402 Google Scholar[5] J. L. Doob, Stochastic processes, John Wiley & Sons Inc., New York, 1953viii+654 MR0058896 0053.26802 Google Scholar[6] I. A. Ibragimov and , Yu. V. Linnik, Independent and stationary sequences of random variables, Wolters-Noordhoff Publishing, Groningen, 1971, 443– MR0322926 0219.60027 Google Scholar[7] William Feller, An introduction to probability theory and its applications. Vol. II., Second edition, John Wiley & Sons Inc., New York, 1971xxiv+669 MR0270403 0219.60003 Google Scholar[8] K. L. Chung, Homogeneous Markov Chains with Countable Numbers of States, Izd-vo “Mir”, Moscow, 1964, (In Russian.) Google Scholar[9] P. Erdös, , W. Feller and , H. Pollard, A property of power series with positive coefficients, Bull. Amer. Math. Soc., 55 (1949), 201–204 MR0027867 0032.27802 CrossrefGoogle Scholar[10] T. E. Harris, The existence of stationary measures for certain Markov processes, Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 1954–1955, vol. II, University of California Press, Berkeley and Los Angeles, 1956, 113–124 MR0084889 0072.35201 Google Scholar[11] S. Orey, Recurrent Markov chains, Pacific J. Math., 9 (1959), 805–827 MR0125632 0095.32902 CrossrefGoogle Scholar[12] Benton Jamison and , Steven Orey, Markov chains recurrent in the sense of Harris, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 8 (1967), 41–48 10.1007/BF00533943 MR0215370 0153.19802 CrossrefGoogle Scholar[13] N. C. Jain, Some limit theorems for a general Markov process, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 6 (1966), 206–223 10.1007/BF00531804 MR0216580 0234.60086 CrossrefGoogle Scholar[14] Stephen R. Kimbleton, A stable limit theorem for Markov chains, Ann. Math. Statist., 40 (1969), 1467–1473 MR0245098 0192.55103 CrossrefGoogle Scholar[15] M. Rosenblatt, A strong mixing condition and a central limit theorem on compact groups, J. Math. Mech., 17 (1967), 189–198 MR0212845 0153.47304 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Age of Information Process under Strongly Mixing Communication - Moment Bound, Mixing Rate and Strong Law Cross Ref Spectral estimation of Hawkes processes from count dataThe Annals of Statistics, Vol. 50, No. 3 Cross Ref Detecting systematic anomalies affecting systems when inputs are stationary time series17 February 2022 | Applied Stochastic Models in Business and Industry, Vol. 38, No. 3 Cross Ref A Semiparametric Approach for Modeling Partially Linear Autoregressive Model with Skew Normal InnovationsAdvances in Mathematical Physics, Vol. 2022 Cross Ref Variable selection via quantile regression with the process of Ornstein-Uhlenbeck type9 September 2021 | Science China Mathematics, Vol. 2 Cross Ref Subgeometric ergodicity and β -mixing16 September 2021 | Journal of Applied Probability, Vol. 58, No. 3 Cross Ref Extremal clustering in non-stationary random sequences12 May 2021 | Extremes, Vol. 3 Cross Ref A new CLT for additive functionals of Markov chainsStochastic Processes and their Applications, Vol. 130, No. 9 Cross Ref Functional CLT for nonstationary strongly mixing processesStatistics & Probability Letters, Vol. 156 Cross Ref Detecting Systematic Anomalies Affecting Systems When Inputs Are Stationary Time SeriesSSRN Electronic Journal Cross Ref A semiparametric approach for modelling multivariate nonlinear time series23 July 2019 | Canadian Journal of Statistics, Vol. 47, No. 4 Cross Ref Power periodic threshold GARCH model: Structure and estimation29 December 2018 | Communications in Statistics - Theory and Methods, Vol. 48, No. 19 Cross Ref Commercial and Residential Mortgage Defaults: Spatial Dependence with FrailtyJournal of Econometrics, Vol. 212, No. 1 Cross Ref A Semiparametric Estimation for the First-Order Nonlinear Autoregressive Time Series Model with Independent and Dependent Errors1 March 2018 | Iranian Journal of Science and Technology, Transactions A: Science, Vol. 43, No. 3 Cross Ref Nonparametric inference on Lévy measures of compound Poisson-driven Ornstein-Uhlenbeck processes under macroscopic discrete observationsElectronic Journal of Statistics, Vol. 13, No. 2 Cross Ref Transformed Perturbation Solutions for Dynamic Stochastic General Equilibrium ModelsSSRN Electronic Journal Cross Ref Estimation and HAC-based Inference for Machine Learning Time Series RegressionsSSRN Electronic Journal Cross Ref On the History of the St. Petersburg School of Probability and Statistics. 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