The Law of the Iterated Logarithm for a Class of Dependent Random Variables

Previous article Next article The Law of the Iterated Logarithm for a Class of Dependent Random VariablesM. IosifescuM. Iosifescuhttps://doi.org/10.1137/1113034PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] J. R. Blum, , D. L. Hanson and , L. H. Koopmans, On the strong law of large numbers for a class of stochastic processes, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 2 (1963), 1–11 MR0161369 (28:4576) 0117.35603 CrossrefGoogle Scholar[2] H. Cohn, Sur les propriétés asymptotiques des systèmes à liaisons complètes, Bull. Math. Soc. Sci. Math. Phys. R. P. Roumaine, 8 (56) (1964), 7–21 MR0207033 (34:6849) 0171.16105 Google Scholar[3] Harry Cohn, On a class of dependent random variables, Rev. Roumaine Math. Pures Appl., 10 (1965), 1593–1606 MR0205305 (34:5136) 0203.19403 Google Scholar[4] P. L. Debruschin, A central limit theorem for nonstationary Markov chains. I, II, Theory Prob. Applications, 1 (1956), 65–80, pp. 329–383 10.1137/1101006 LinkGoogle Scholar[5] W. Doeblin, Sur les propriétés asymptotiques des mouvements régis par certains types de chaı⁁nes simples, Bull. Math. Soc. Roumaine Sci., 39 (57–115), 1937–, 39, 2 (1937), pp. 3–61 Google Scholar[6] E. B. Dynkin, On some limit theorems for Markov chains, Ukrain. Mat. Ž., 6 (1954), 21–27, (In Russian.) MR0076219 (17,866b) Google Scholar[7] Carl-Gustav Esseen, Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian law, Acta Math., 77 (1945), 1–125 MR0014626 (7,312a) 0060.28705 CrossrefGoogle Scholar[8] I. A. Ibragimov, Some limit theorems for stationary processes, Theory Prob. Applications, 7 (1962), 349–382 10.1137/1107036 0119.14204 LinkGoogle Scholar[9] M. Iosifesku, Random systems with complete connections with an arbitrary state space, Rev. Math. Pures Appl. (Bucarest), 8 (1963), 611–645, (In Russian.) MR0179829 (31:4070) Google Scholar[10] Marius Iosifescu, Sur les coefficients dits “d'ergodicité”, C. R. Acad. Sci. Paris, 260 (1965), 5678–5680 MR0182994 (32:476) 0125.36901 Google Scholar[11] Marius Iosifescu, On the uniform ergodicity of a class of nonhomogeneous random systems with complete connections, Rev. Roumaine Math. Pures Appl., 11 (1966), 763–772 MR0214125 (35:4976) Google Scholar[12] Michel Loève, Probability theory, 2nd ed. The University Series in Higher Mathematics. D. Van Nostrand Co., Inc., Princeton, N. J.-Toronto-New York-London, 1960xvi+685 MR0123342 (23:A670) 0095.12201 Google Scholar[13] O. Onicescu and , G. Mihoc, Sur les chaı⁁nes de variables statistiques, Bull. Sci. Math., 59 (1935), 174–192 0012.02804 Google Scholar[14A] Tadashi Ueno, Some limit theorems for temporally discrete Markov processes, J. Fac. Sci. Univ. Tokyo. Sect. I., 7 (1957), 449–462 MR0090921 (19,891a) 0077.33201 Google Scholar[14B] Tadashi Ueno, Some limit theorems for temporally discrete Markov processes. II, J. Fac. Sci. Univ. Tokyo. Sect. I, 7 (1958), 557–565 MR0097125 (20:3604b) 0080.34602 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Invariance Principles for the Law of the Iterated Logarithm for Martingales and Processes with Stationary Increments24 June 2010 Cross Ref A Central Limit Theorem and Law of the Iterated Logarithm for a Random Field with Exponential Decay of Correlations20 November 2018 | Canadian Journal of Mathematics, Vol. 56, No. 1 Cross Ref Approximation of Distributions of Sums of Weakly Dependent Random Variables by the Normal Distribution Cross Ref An almost sure invariance principle for stationary ergodic sequences of Banach space valued random variablesProbability Theory and Related Fields, Vol. 84, No. 2 Cross Ref Convergence rates in the central limit theorem for stationary mixing sequences of random vectorsJournal of Multivariate Analysis, Vol. 9, No. 4 Cross Ref The Borel-Cantelli lemma for strong mixing sequences of events and their applications to LILKodai Mathematical Journal, Vol. 2, No. 2 Cross Ref On Strassen's version of the loglog law for some classes of dependent random variablesZeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 24, No. 2 Cross Ref Note on the law of the iterated logarithm for stationary processes satisfying mixing conditionsKodai Mathematical Journal, Vol. 23, No. 3 Cross Ref Volume 13, Issue 2| 1968Theory of Probability & Its Applications History Submitted:04 May 1968Published online:28 July 2006 InformationCopyright © 1968 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1113034Article page range:pp. 304-313ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics