Convergence of Numerical Characteristics of Sums of Independent Random Variables with Values in a Hilbert Space

Previous article Next article Convergence of Numerical Characteristics of Sums of Independent Random Variables with Values in a Hilbert SpaceV. N. KruglovV. N. Kruglovhttps://doi.org/10.1137/1118091PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] S. N. Bernstein, Collected Works, Vol. 4, Izd-vo “Nauka”, Moscow, 1964, (In Russian.) Google Scholar[2] N. N. Bakhaniya, Probability Distributions in Linear Spaces, Izd-vo Metsniereba, Tbilisi, 1971, (In Russian.) Google Scholar[3] I. I. Gikhman and , A. V. Skorohod, The theory of stochastic processes. I, Springer-Verlag, New York, 1974viii+570 MR0346882 (49:11603) 0291.60019 CrossrefGoogle Scholar[4] A. V. Skorohod, Random Processes with Independent Increments, Izd-vo “Nauka”, Moscow, 1964, (In Russian.) Google Scholar[5] Yu. V. Prokhorov, Convergence of random processes and limit theorems in probability theory, Theory Prob. Applications, 1 (1956), 157–214 10.1137/1101016 LinkGoogle Scholar[6] Yu. 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Statist., 41 (1970), 1853–1860 MR0295414 (45:4480) 0216.46103 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Glivenko–Cantelli Theorem and Bernstein–Kantorovich Invariance Principle12 November 2012 Cross Ref Probability Distances and Probability Metrics: Definitions12 November 2012 Cross Ref Probability Distances and Metrics20 April 2011 Cross Ref Tauberian Theorems and Asymptotics of Infinitely Divisible Distributions in a ConeA. L. Yakymiv25 July 2006 | Theory of Probability & Its Applications, Vol. 48, No. 3AbstractPDF (169 KB)Strong Limit Theorems for Mixing Random Variables with Values in Hilbert Space and their Applications Cross Ref Limiting properties of order statisticsJournal of Soviet Mathematics, Vol. 53, No. 6 Cross Ref The Convergence of Moments in a Random Limit Theorem of H. Robbins’ TypeK. S. Kubacki and D. 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Lifshits17 July 2006 | Theory of Probability & Its Applications, Vol. 20, No. 4AbstractPDF (1156 KB) Volume 18, Issue 4| 1974Theory of Probability & Its Applications History Submitted:20 July 1972Published online:28 July 2006 InformationCopyright © 1974 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1118091Article page range:pp. 694-712ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics