The Contraction Principle and the Strong Law of Large Numbers for Weighted Sums
V. V. Buldygin, S. A. Solntsev · Theory of Probability and Its Applications · 1987
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