Large Deviations in Banach Spaces

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Previous article Next article Large Deviations in Banach SpacesV. Yu. BentkusV. Yu. Bentkushttps://doi.org/10.1137/1131085PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] V. V. Jurinsky, Exponential inequalities for sums of random vectors, J. Multivariate Anal., 6 (1976), 473–499 10.1016/0047-259X(76)90001-4 55:1422 0346.60001 CrossrefGoogle Scholar[2] L. V. Osipov, On large deviations for sums of independent random vectors, Summary of Reports of the 2nd International Vil'nius Conference on Probability Theory and Mathematical Statistics, Vol. 2, Inst. Mat. i Kib. Akad. Nauk Litovsk. SSR, Vil'nius, 95–96, (In Russian.) Google Scholar[3] V. A. Statulyavichus, , R. Rudzkis and , L. Saulis, Large deviations for sums of independent random variables, Lithuanian Math. J., 19 (1979), 118–125 CrossrefGoogle Scholar[4] V. A. Statulyavichus, , R. Rudzkis and , L. Saulis, A general lemma on probabilities of large deviations, Lithuanian Math. J., 18 (1978), 226–238 0423.60027 CrossrefGoogle Scholar[5] V. V. Petrov, Sums of independent random variables, Springer-Verlag, New York, 1975x+346, Berlin–Heidelberg 52:9335 0322.60042 CrossrefGoogle Scholar[6] V. Bentkus and , A. Rachkauskas, Estimates of the rate of convergence for sums of independent random variables in a Banach space, Lithuanian Math. J., 22 (1982), 222–234 CrossrefGoogle Scholar[7] V. Bentkus and , A. Rachkauskas, Estimates of the rate of convergence for sums of independent random variables in a Banach space, II, Lithuanian Math. J., 22 (1982), 349–353 CrossrefGoogle Scholar[8] V. V. Sazonov, Normal approximation—some recent advances, Lecture Notes in Mathematics, Vol. 879, Springer-Verlag, Berlin, 1981, 1–105 83g:60035 0462.60006 Google Scholar[9] J. Kuelbs and , T. Kurtz, Berry-Esseen estimates in Hilbert space and an application to the law of the iterated logarithm, Ann. Probability, 2 (1974), 387–407 50:14868 0298.60017 CrossrefGoogle Scholar[10] V. I. Paulauskas, On the rate of convergence in the central limit theorem in certain Banach spaces, Theory Probab. Appl., 21 (1976), 754–769 10.1137/1121088 0403.60007 LinkGoogle Scholar[11] V. V. Ulyanov, On refinement of proximity estimates for two distributions of sums of independent Banach-valued random values, Vestnik Moskov. Univ., Ser. Vyschisl. Mat. Kibernet., 1 (1981), 50–57, (In Russian.) Google Scholar[12] Vygantas Paulaskas, On the approximation of indicator functions by smooth functions in Banach spacesFunctional analysis and approximation (Oberwolfach, 1980), Internat. Ser. Numer. Math., Vol. 60, Birkhäuser, Basel, 1981, 385–394 83d:60013 0475.41034 CrossrefGoogle Scholar[13] V. Yu. Bentkus, Lower bounds for the rate of convergence in the central limit theorem in Banach spaces, Lith. Math. J., 25 (1985), 312–320 0659.60018 CrossrefGoogle Scholar[14] V. M. Zolotarev, Concerning a certain probability problem, Theory Probab. Appl., 6 (1981), 201–204 10.1137/1106025 0109.36404 LinkGoogle Scholar[15] W. Hoeffding, On a theorem of V. M. Zolotarev, Theory Probab. Appl., 9 (1964), 89–91 10.1137/1109008 LinkGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails High-dimensional CLT: Improvements, non-uniform extensions and large deviationsBernoulli, Vol. 27, No. 1 Cross Ref Extreme biases in prime number races with many contestants21 February 2019 | Mathematische Annalen, Vol. 374, No. 1-2 Cross Ref Theorems of Large Deviations for the Sums of a Random Number of Independent Random Variables, Vol. 56 Cross Ref Large deviations for martingales via Cramér's methodStochastic Processes and their Applications, Vol. 85, No. 2 Cross Ref On moderate deviations for martingalesThe Annals of Probability, Vol. 25, No. 1 Cross Ref Large deviations for martingales with some applicationsActa Applicandae Mathematicae, Vol. 38, No. 1 Cross Ref On Large Deviation Asymptotics in Hilbert Space I17 July 2006 | Theory of Probability & Its Applications, Vol. 36, No. 1AbstractPDF (1505 KB)Probabilities of Large Deviations in Hilbert space17 July 2006 | Theory of Probability & Its Applications, Vol. 34, No. 4AbstractPDF (523 KB)The Accuracy of Gaussian Approximation in Banach Spaces17 July 2006 | Theory of Probability & Its Applications, Vol. 34, No. 4PDF (229 KB) Volume 31, Issue 4| 1987Theory of Probability & Its Applications History Submitted:08 April 1986Published online:17 July 2006 InformationCopyright © 1987 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1131085Article page range:pp. 627-632ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics