On Limit Theorems for Sums of Dependent Random Variables

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Previous article Next article On Limit Theorems for Sums of Dependent Random VariablesA. F. RonzhinA. F. Ronzhinhttps://doi.org/10.1137/1124064PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Z. A. Lomnicki and , S. C. Zaremba, A further instance of the central limit theorem for dependent random variables, Math. Z, 66 (1957), 490–494 10.1007/BF01186625 MR0099714 0077.33101 CrossrefGoogle Scholar[2] C. Serge, Graphs and Hypergraphs, American Elsevier, New York, 1973 0254.05101 Google Scholar[3] B. I. Selivanov, The generating function of a certain statistic in a multinomial scheme with a countable number of outcomes, Kombinatornyi˘ Anal., (1972), 11–16 MR0451338 Google Scholar[4] B. I. Selivanov, Enumeration of homogeneous hypergraphs with a simple cycle structure, Kombinatornyi˘ Anal., (1972), 60–67 MR0480173 Google Scholar[5] 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[6] A. Kofman, Vvedenie v prikladnuyu kombinatoriku, Izdat. “Nauka”, Moscow, 1975, 479– MR0373910 Google Scholar[7] V. G. Mihai˘lov, The central limit theorem for inhomogeneous U-statistics of finitely dependent random variables, Mat. Sb. (N.S.), 98(140) (1975), 624–634, 640 MR0402865 Google Scholar[8] Richard Bellman, Introduction to matrix analysis, Second edition, McGraw-Hill Book Co., New York, 1970xxiii+403 MR0258847 0216.06101 Google Scholar[9] V. G. Mikhailov, Central limit theorem for the number of incomplete long repetitions, Theory Prob. Appl., 20 (1975), 862–866 10.1137/1120094 0352.60017 LinkGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails A Functional Limit Theorem for Homogeneous U-Statistics with a Degenerate KernelA. F. Ronzhin28 July 2006 | Theory of Probability & Its Applications, Vol. 30, No. 4AbstractPDF (417 KB)On a Condition for Slowly Growing Number of DependenciesA. M. Leontovich28 July 2006 | Theory of Probability & Its Applications, Vol. 30, No. 1AbstractPDF (623 KB)An approximation for the inverse distribution function of a combination of random variables, with an application to operating theatres †Journal of Statistical Computation and Simulation, Vol. 23, No. 3 Cross Ref On Two Statistics in the Multinomial SchemeA. F. Ronzhin28 July 2006 | Theory of Probability & Its Applications, Vol. 28, No. 4AbstractPDF (547 KB)The Central Limit Theorem for a Sequence of Random Variables with a Slowly Growing Number of DependencesM. B. Petrovskaya and A. M. Leontovich17 July 2006 | Theory of Probability & Its Applications, Vol. 27, No. 4AbstractPDF (884 KB)Asymptotic Formulas for the Moments of U-Statistics with Degenerate KernelA. F. Ronzhin17 July 2006 | Theory of Probability & Its Applications, Vol. 27, No. 1AbstractPDF (807 KB) Volume 24, Issue 3| 1980Theory of Probability & Its Applications History Submitted:13 September 1977Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1124064Article page range:pp. 549-559ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics