Next article Limit Theorems for Sums of Independent Random Variables with Values in Hilbert SpaceV. M. KruglovV. M. Kruglovhttps://doi.org/10.1137/1117026PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Vladimir M. Zolotarev, Théorèmes limites généraux pour les sommes de variables aléatoires indépendantes, C. R. Acad. Sci. Paris Sér. A-B, 270 (1970), A899–A902 MR0261671 0212.50101 Google Scholar[2] Juozas Mačys, Sur la convergence des répartitions de sommes de variables aléatoires indépendantes vers les lois de la classe $I\sb{0}$ de Linnik, C. R. Acad. Sci. Paris Sér. A-B, 267 (1968), A316–A317 MR0233401 0164.48204 Google Scholar[3] 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[4] K. R. Parthasarathy, Probability measures on metric spaces, Probability and Mathematical Statistics, No. 3, Academic Press Inc., New York, 1967xi+276, London MR0226684 0153.19101 CrossrefGoogle Scholar[5] Yu. V. Linnik, Decompositions of Probability Laws, Izd-vo Leningr. Un-ta, 1960, (In Russian.) Google Scholar[6] U. Grenander, Probabilities on Algebraic Structures, Izd-vo “Mir”, Moscow, 1965 0139.33401 Google Scholar[7] 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 0095.12201 Google Scholar Next article FiguresRelatedReferencesCited byDetails A functional central limit theorem for Hilbert-valued martingales5 April 2016 | Lobachevskii Journal of Mathematics, Vol. 37, No. 2 Cross Ref Reflections on the Classical Theory of Limit TheoremsV. M. Zolotarev17 July 2006 | Theory of Probability & Its Applications, Vol. 36, No. 1AbstractPDF (1793 KB)VIII Seminar on Problems of Stability of Stochastic Models17 July 2006 | Theory of Probability & Its Applications, Vol. 30, No. 3AbstractPDF (1130 KB)On the Invariance Principle for Semi-Martingales: The “Nonclassical” CaseR. Sh. Liptser and A. N. Shiryaev17 July 2006 | Theory of Probability & Its Applications, Vol. 28, No. 1AbstractPDF (1908 KB)On a Class of Limit LawsE. Hensz and R. Jajte17 July 2006 | Theory of Probability & Its Applications, Vol. 23, No. 1AbstractPDF (560 KB)Global Limit TheoremsV. M. Kruglov17 July 2006 | Theory of Probability & Its Applications, Vol. 21, No. 1AbstractPDF (414 KB)Convergence of Numerical Characteristics of Sums of Independent Random Variables with Values in a Hilbert SpaceV. N. Kruglov28 July 2006 | Theory of Probability & Its Applications, Vol. 18, No. 4AbstractPDF (1380 KB) Volume 17, Issue 2| 1973Theory of Probability & Its Applications History Submitted:12 June 1969Published online:17 July 2006 InformationCopyright © 1973 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1117026Article page range:pp. 199-217ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics