On the Dependence of the Convergence Rate in the Strong Law of Large Numbers for Stationary Processes on the Rate of Decay of the Correlation Function

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Previous article Next article On the Dependence of the Convergence Rate in the Strong Law of Large Numbers for Stationary Processes on the Rate of Decay of the Correlation FunctionV. F. GaposhkinV. F. Gaposhkinhttps://doi.org/10.1137/1126078PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] André Blanc-Lapierre and , Albert Tortrat, Sur la loi forte des grands nombres pour les fonctions aléatoires stationnaires du second ordre, C. R Acad. Sci. Paris Sér. A-B, 267 (1968), A740–A743 39:4924 0177.46103 Google Scholar[2] I. N. Verbitskaya, On conditions for the applicability of the strong law of large numbers to wide-sense stationary processes, Theory Prob. Appl., 11 (1966), 632–636 LinkGoogle Scholar[3] V. V. Petrov, The strong law of large numbers for a stationary sequence, Dokl. Akad. Nauk SSSR, 213 (1973), 42–44, (In Russian.) 49:4083 0303.60032 Google Scholar[4] R. J. Serfling, Moment inequalities for the maximum cumulative sum, Ann. Math. Statist., 41 (1970), 1227–1234 42:3835 0272.60013 CrossrefGoogle Scholar[5] V. F. Gaposhkin, Convergence of series that are connected with stationary sequences, Izv. Akad. Nauk SSSR Ser. Mat., 39 (1975), 1366–1392, 1438, (In Russian.) 53:6694 Google Scholar[6] V. F. Gaposhkin, Criteria for the strong law of large numbers for some classes of second-order stationary processes and homogeneous random fields, Theory Prob. Appl., 22 (1977), 286–310 0377.60033 LinkGoogle Scholar[7] V. F. Gaposhkin, Exact estimates of the rate of convergence in the strong law of large numbers for classes of stationary (in the wide sense) sequences and processes, Uspehi Mat. Nauk, 31 (1976), 233–234, (In Russian.) 55:9240 Google Scholar[8] V. F. Gaposhkin, Estimates of means for almost all realizations of stationary processes, Sibirsk. Mat. Zh., 20 (1979), 978–989, 1165, (In Russian.) 82d:60064 0447.60028 Google Scholar[9] G. Aleksich, Problems in the Convergence of Orthogonal Series, IL, Moscow, 1963, (In Russian.) Google Scholar[10] A. Zygmund, Trigonometrical Series, 2 vols., Cambridge University Press, Cambridge, 1959 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Exponent of Convergence of a Sequence of Ergodic Averages26 August 2022 | Mathematical Notes, Vol. 112, No. 1-2 Cross Ref Weighted laws of large numbers and convergence of weighted ergodic averages on vector valued $$L_p$$-spaces5 July 2021 | Advances in Operator Theory, Vol. 6, No. 3 Cross Ref Constructive approach to limit theorems for recurrent diffusive random walks on a stripAsymptotic Analysis, Vol. 122, No. 3-4 Cross Ref Almost everywhere convergence of ergodic series6 October 2015 | Ergodic Theory and Dynamical Systems, Vol. 37, No. 2 Cross Ref Pointwise equidistribution with an error rate and with respect to unbounded functions4 April 2016 | Mathematische Annalen, Vol. 367, No. 1-2 Cross Ref An effective Ratner equidistribution result for SL(2,R)⋉R2Duke Mathematical Journal, Vol. 164, No. 5 Cross Ref On Estimates of the Convergence Rate in the Strong Law of Large Numbers for Stationary Sequences (in Some Classes $S_w$ and $R_\Phi$)V. F. Gaposhkin10 November 2011 | Theory of Probability & Its Applications, Vol. 55, No. 4AbstractPDF (194 KB)POINTWISE ERGODIC THEOREMS WITH RATE WITH APPLICATIONS TO LIMIT THEOREMS FOR STATIONARY PROCESSES21 November 2011 | Stochastics and Dynamics, Vol. 11, No. 01 Cross Ref Pointwise ergodic theorems with rate and application to the CLT for Markov chainsAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques, Vol. 45, No. 3 Cross Ref Extensions of the Menchoff-Rademacher theorem with applications to ergodic theoryIsrael Journal of Mathematics, Vol. 148, No. 1 Cross Ref Fractional Poisson equations and ergodic theorems for fractional coboundariesIsrael Journal of Mathematics, Vol. 123, No. 1 Cross Ref Volume 26, Issue 4| 1982Theory of Probability & Its Applications History Submitted:18 December 1979Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1126078Article page range:pp. 706-720ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics