On an Infinite-Dimensional Version of S. N. Bernstein’s Inequalities
V. V. Yurinskii · Theory of Probability and Its Applications · 1970
Previous article Next article On an Infinite-Dimensional Version of S. N. Bernstein’s InequalitiesV. V. YurinskiiV. V. Yurinskiihttps://doi.org/10.1137/1115008PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout"On an Infinite-Dimensional Version of S. N. Bernstein’s Inequalities." Theory of Probability & Its Applications, 15(1), pp. 108–109[1] Yu. V. Prokhorov, Extension of S. N. Bernstein's inequality to the multidimensional case, Theory of Prob. Applications, 13 (1968), 266–274 0181.45102 Google Scholar[2] Yu. V. Prokhorov, The inequality of S. N. Bernstein in the multidimensional case, Theory of Prob. Applications, 13 (1968), 462–470 0181.45102 Google Scholar[3] S. N. Bernstein, Theory of Probability, Goztehizdat, Moscow–Leningrad, 1946 Google Scholar[4] A. N. Kolmogorov, Über das Gesetz des iterierten Logarithmus, Math. Ann., 109 (1928), 26–37 Google Scholar[5] Wassily Hoeffding, Probability inequalities for sums of bounded random variables, J. Amer. Statist. Assoc., 58 (1963), 13–30 MR0144363 0127.10602 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails A large deviation inequality for vector functions on finite reversible Markov ChainsThe Annals of Applied Probability, Vol. 17, No. 4 Cross Ref On the Monotonicity of Exact Upper Sequences for Sums of Independent Random Vectors in Hilbert Space17 July 2006 | Theory of Probability & Its Applications, Vol. 33, No. 1AbstractPDF (330 KB)Remarks on Inequalities for Large Deviation Probabilities28 July 2006 | Theory of Probability & Its Applications, Vol. 30, No. 1AbstractPDF (539 KB)Estimates of Characteristic Functions of Certain Random Variables with Application to $\omega ^2 $-Statistics. I17 July 2006 | Theory of Probability & Its Applications, Vol. 29, No. 3AbstractPDF (1126 KB)On an Infinite-Dimensional Central Limit Theorem17 July 2006 | Theory of Probability & Its Applications, Vol. 29, No. 2AbstractPDF (826 KB)On the Limit Behavior of Sums of Random Vectors with Values in Hilbert Space17 July 2006 | Theory of Probability & Its Applications, Vol. 29, No. 3AbstractPDF (289 KB)On the Asymptotic Behavior of Infinitely Divisible Distributions in Banach Space17 July 2006 | Theory of Probability & Its Applications, Vol. 27, No. 4AbstractPDF (1497 KB)Estimate of the Accuracy of Normal Approximation in Hilbert Space17 July 2006 | Theory of Probability & Its Applications, Vol. 27, No. 2AbstractPDF (561 KB)On Large Deviation Probabilities for Sums of Independent Random Vectors17 July 2006 | Theory of Probability & Its Applications, Vol. 23, No. 3AbstractPDF (1498 KB)Inequalities for Random Vectors28 July 2006 | Theory of Probability & Its Applications, Vol. 22, No. 3AbstractPDF (415 KB)On the Error of the Gaussian Approximation for Convolutions17 July 2006 | Theory of Probability & Its Applications, Vol. 22, No. 2AbstractPDF (949 KB)Summary of Papers Presented at Sessions of the Probability and Statistics Section of the Moscow Mathematical Society (February–October 1974)17 July 2006 | Theory of Probability & Its Applications, Vol. 20, No. 2AbstractPDF (1740 KB)Exponential Bounds for Large Deviations28 July 2006 | Theory of Probability & Its Applications, Vol. 19, No. 1PDF (187 KB)Convergence of Numerical Characteristics of Sums of Independent Random Variables with Values in a Hilbert Space28 July 2006 | Theory of Probability & Its Applications, Vol. 18, No. 4AbstractPDF (1380 KB)On Inequalities for Large Deviations for Certain Statistics17 July 2006 | Theory of Probability & Its Applications, Vol. 16, No. 2AbstractPDF (286 KB)Inequalities for the Probabilities of Large Deviations in the Multidimensional Case17 July 2006 | Theory of Probability & Its Applications, Vol. 16, No. 4AbstractPDF (390 KB) Volume 15, Issue 1| 1970Theory of Probability & Its Applications History Submitted:17 September 1969Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1115008Article page range:pp. 108-109ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics