On Convergence of Sums of Operator-Normed Independent Random Vectors

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Previous article Next article On Convergence of Sums of Operator-Normed Independent Random VectorsV. V. Buldygin and S. A. SolntsevV. V. Buldygin and S. A. Solntsevhttps://doi.org/10.1137/1136039PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Yu. V. Prokhorov, On the strong law of large numbers, Izvestiya Akad. Nauk SSSR. Ser. Mat., 14 (1950), 523–536 12,425c Google Scholar[2] Michel Loève, Probability theory, Third edition, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1963xvi+685, New York 34:3596 0108.14202 Google Scholar[3] N. A. Volodin and , S. V. Nagaev, A remark on the strong law of large numbers, Theory Probab. Appl., 22 (1977), 810–822 10.1137/1122092 0391.60038 LinkGoogle Scholar[4] A. I. Martikainen and , V. V. Petrov, On necessary and sufficient conditions for the law of iterated logarithm, Theory Probab. Appl., 22 (1977), 16–24 10.1137/1122002 0377.60036 LinkGoogle Scholar[5] V. V. Buldygin, The strong law of large numbers and convergence to zero of Gaussian sequences, Theory Probab. Math. Statist., (1979), 35–43 0485.60029 Google Scholar[6] A. I. Martikainen, On necessary and sufficient conditions for the strong law of large numbers, Theory Probab. Appl., 24 (1979), 813–819 10.1137/1124093 LinkGoogle Scholar[7] O. M. Yadrenko, The strong law of large numbers with matrix normalization and conditions of convergence to zero for one class of Gaussian sequences, Some Problems in the Theory of Stochastic Processes, Math. Inst. Acad. Nauk Ukrainian SSR, Kiev, (1982), 117–133, (In Russian.) 0543.60037 Google Scholar[8] V. V. Buldygin and , S. A. Solntsev, The SLLN for sums of independent random vectors with operator normalization and null convergence of Gaussian sequences, Theory Probab. Appl., 32 (1987), 243–258 10.1137/1132034 0677.60033 LinkGoogle Scholar[9] S. A. Solntsev, Stochastic stability of linear summation schemes, Deposited at UkrNIINTI, No. 2745-Uk88. (In Russian.) Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Volume 36, Issue 2| 1992Theory of Probability & Its Applications History Submitted:13 February 1989Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1136039Article page range:pp. 360-365ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics