Estimates of the Distance between Sums of Independent Random Elements in Banach Spaces

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Previous article Next article Estimates of the Distance between Sums of Independent Random Elements in Banach SpacesV. Yu. Bentkus and A. RachkauskasV. Yu. Bentkus and A. Rachkauskashttps://doi.org/10.1137/1129005PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] V. M. Zolotarev, Metric distances in spaces of random variables and of their distributions, Math. USSR Sb., 30 (1976), 373–401 0383.60022 CrossrefGoogle Scholar[2] V. M. Zolotarev, Approximation of the distributions of sums of independent random variables with values in infinite-dimensional spaces, Theory Prob. Appl., 21 (1976), 721–737, correction in 22 (1977), p. 881 0378.60003 LinkGoogle Scholar[3] A. S. Nemirovskii and , S. M. Semenov, On polynomial approximation of functions on Hilbert space, Math. USSR Sb., 21 (1973), 255–278 0288.41023 CrossrefGoogle Scholar[4] V. Yu. Bentkus and , A. Rachkauskas, Estimates of the rate of convergence of sums of independent random variables in a Banach space. I, Lithuanian Math. J., 22 (1982), 222–234 0522.60007 V. Yu. Bentkus and , A. Rachkauskas, Estimates of the rate of convergence of sums of independent random variables in a Banach space. II, Lithuanian Math. J., 22 (1982), 344–353 0522.60008 CrossrefGoogle Scholar[5] V. Yu. Bentkus and , A. Rachkauskas, On the rate of convergence in the central limit theorem in infinite-dimensional spaces, Lithuanian Math. J., 21 (1981), 271–277 0518.60008 CrossrefGoogle Scholar[6] V. Yu. Bentkus, Estimates of closeness for sums of independent random elements in the space $C[0,1]$, Litovsk. Mat. Sb., 23 (1983), 7–16, (In Russian.) Google Scholar[7] P. P. Gudinas, On the use of metrics of type ζ in limit theorems for weakly dependent random elements, Abstracts, 3rd Internat. Vil'nius Conference on Probability Theory and Mathematical Statistics, Vol. 1, Inst. Matematiki i Kibernetiki Akad. Nauk Litovsk. SSR, Vilnius, 1981, 151–152, (In Russian.) Google Scholar[8] V. V. Senatov, Some lower estimates for the rate of convergence in the central limit theorem in Hilbert space, Soviet Math. Dokl., 23 (1981), 188–192 0474.60007 Google Scholar[9] R. Lapinskas, On the approximation of partial sums in certain Banach spaces, Lithuanian Math. J., 18 (1978), 494–498 0412.60011 CrossrefGoogle Scholar[10] V. M. Zolotarev, Ideal metrics in the problem of approximating the distributions of sums of independent random variables, Theory Prob. Appl., 22 (1977), 433–449. 0385.60025 Google Scholar[11] G. Pisier, Le théorèms de la limits centrâle et la loi de logarithms itéré dans les espaces de Banach, 1975–1976, Sém. Maurey-Schwartz, exp III Google Scholar[12] V. V. Yurinskii, On the error in Gaussian approximation of convolutions, Theory Prob. Appl., 22 (1977), 236–247 LinkGoogle Scholar[13] A. G. Kukush, Weak convergence of measures and convergence of semi-invariants, Theory Probab. Math. Statist., 23 (1981), 79–86 0482.28010 Google Scholar[14] A. G. Kukush, The central limit theorem in Hilbert space in terms of the Lévy-Prokhorov metric, Theory Probab. Math. Statist., 25 (1982), 61–68 0504.60009 Google Scholar[15] R. M. Dudley, Distances of probability measures and random variables, Ann. Math. Statist, 39 (1968), 1563–1572 37:5900 0169.20602 CrossrefGoogle Scholar[16] G. P. Yamukov, Estimates for generalized Dudley metrics in spaces of finite-dimensional distributions, Theory prob. Appl., 22 (1977), 579–584 0386.60022 LinkGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails On a functional contraction methodThe Annals of Probability, Vol. 43, No. 4 Cross Ref Ideal Metric with Respect to Maxima Scheme of i.i.d. Random Elements12 November 2012 Cross Ref A functional limit theorem for the profile of search treesThe Annals of Applied Probability, Vol. 18, No. 1 Cross Ref A New Way to Obtain Estimates in the Invariance Principle Cross Ref On the rate of convergence in the martingale CLTStatistics & Probability Letters, Vol. 23, No. 3 Cross Ref Geometric stable distributions in Banach spacesJournal of Theoretical Probability, Vol. 7, No. 2 Cross Ref Rate of Convergence for Sums and Maxima and Doubly Ideal MetricsS. T. Rachev and L. Rüschendorf28 July 2006 | Theory of Probability & Its Applications, Vol. 37, No. 2AbstractPDF (1313 KB) Volume 29, Issue 1| 1985Theory of Probability & Its Applications History Submitted:29 October 1981Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1129005Article page range:pp. 50-65ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics