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• W2068998768 abstract "Previous article Next article The Contraction Principle and the Strong Law of Large Numbers for Weighted SumsV. V. Buldygin and S. A. SolntsevV. V. Buldygin and S. A. Solntsevhttps://doi.org/10.1137/1131059PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] N. N. Vakhaniya, Probability distributions on linear spaces, North-Holland Publishing Co., New York, 1981xv+123 82i:60015 0481.60002 Google Scholar[2] V. V. Buldygin and , S. S. Solntsev, Oscillatory properties of Gaussian sequencesProbabilistic infinite-dimensional analysis, Akad. Nauk Ukrain. SSR Inst. Mat., Kiev, 1981, 15–29, 123, (In Russian.) 84a:60050 0503.60049 Google Scholar[3] Jean-Pierre Kahane, Some random series of functions, D. C. Heath and Co. Raytheon Education Co., Lexington, Mass., 1968viii+184, Boston 40:8095 0192.53801 Google Scholar[4] J. Hoffmann-Jorgensen, Sums of independent Banach space valued random variables, Studia Math., 52 (1974), 159–186 50:8626 0265.60005 CrossrefGoogle Scholar[5] Naresh C. Jain and , Michael B. Marcus, Integrability of infinite sums of independent vector-valued random variables, Trans. Amer. Math. Soc., 212 (1975), 1–36 52:6854 0318.60036 CrossrefGoogle Scholar[6] V. V. Buldygin and , N. A. Pidsukha, Comparison theorems for random series in Banach spaces and some schemes of summation, Theory Probab. Appl., 23 (1978), 22–35 10.1137/1123002 0423.60006 LinkGoogle Scholar[7] V. V. Buldygin, Convergence of Random Elements in Topological Spaces, Naukova Dumka, Kiev, 1980, (In Russian.) 0512.60009 Google Scholar[8] G. M. Fikhtengol'ts, A Course of Differential and Integral Calculus, Vol. 2, Nauka, Moscow, 1966, (In Russian.) Google Scholar[9] Kiyosi Itô and , Makiko Nisio, On the convergence of sums of independent Banach space valued random variables, Osaka J. Math., 5 (1968), 35–48 38:3897 0177.45102 Google Scholar[10] V. V. Buldygin, Certain properties of random series in Banach spaces, Teor. Verojatnost. i Mat. Statist., (1973), 37–46, 174, (In Russian.) 54:1331 Google Scholar[11] E. I. Ostrovskii, On the supports of probability measures in separable Banach spaces, Dokl. Akad. Nauk SSSR, 255 (1980), 1319–1320, (In Russian.) 82c:60013 Google Scholar[12] Robert L. Taylor, Stochastic convergence of weighted sums of random elements in linear spaces, Lecture Notes in Mathematics, Vol. 672, Springer, Berlin, 1978vii+216 80g:60006 0443.60004 Google Scholar[13] Ulf Grenander, Probabilities on algebraic structures, John Wiley & Sons Inc., New York, 1963, 218– 34:6810 0131.34804 Google Scholar[14] Yu. V. Prokhorov, On the strong law of large numbers, Izvestiya Akad. Nauk SSSR. Ser. Mat., 14 (1950), 523–536, (In Russian.) 12,425c Google Scholar[15] Michel Loève, Probability theory, Third edition, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1963xvi+685 34:3596 0108.14202 Google Scholar[16] A. I. Martikainen and , V. V. Petrov, On necessary and sufficient conditions for the law of the iterated logarithm, Theory Probab. Appl., 22 (1977), 16–23 10.1137/1122002 0377.60036 LinkGoogle Scholar[17] V. V. Buldygin, The strong law of large numbers and the convergence to zero of Gaussian sequences, Teor. Verojatnost. i Mat. Statist., (1978), 33–41, 156–157, (In Russian.) 58:13294 Google Scholar[18] 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[19] I. M. Gelfand, Lectures on Linear Algebra, Nauka, Moscow, 1966, (In Russian.) Google Scholar[20] O. M. Yadrenko, Masters Thesis, Laws of large numbers in linear spaces, author's abstract of candidate's dissertation, Ukrain. Math. Institute, Kiev, 1984, (In Russian.) Google Scholar[21] Rafał Sztencel, On boundedness and convergence of some Banach space valued random series, Probab. Math. Statist., 2 (1981), 83–88 83a:60019 0505.60015 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails On the limiting behavior of randomly weighted partial sumsStatistics & Probability Letters, Vol. 40, No. 4 | 1 Nov 1998 Cross Ref On Sample Continuity of Multidimensional Gaussian Markov ProcessesTheory of Probability & Its Applications, Vol. 38, No. 4 | 17 July 2006AbstractPDF (1057 KB)The Strong Law of Large Numbers for Sums of Independent Random Vectors with Operator Normalizations and Null Convergence of Gaussian SequencesTheory of Probability & Its Applications, Vol. 32, No. 2 | 17 July 2006AbstractPDF (1225 KB) Volume 31, Issue 3| 1987Theory of Probability & Its Applications375-562 History Submitted:24 July 1984Published online:28 July 2006 InformationCopyright © 1987 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1131059Article page range:pp. 452-462ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics" @default.
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