Previous article Next article On Large Deviation Asymptotics in Hilbert Space IV. V. YurinskyV. V. Yurinskyhttps://doi.org/10.1137/1136008PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] V. M. Zolotarev, Concerning a certain probability problem, Theory Probab. Appl., 6 (1961), 201–203 10.1137/1106025 0109.36404 LinkGoogle Scholar[2] W. Hoeffding, On a theorem of V. M. Zolotarev, Theory Probab. Appl., 9 (1964), 89–91 10.1137/1109008 LinkGoogle Scholar[3] L. V. Osipov, On large deviations for sums of independent random vectors, Abstracts of Commun. 2nd Vilnius Conf. on Probab. and Statist., Vilnius, 1977, June–July, IMC, Vilnius, 2 (1977), pp. 95–96. (In Russian.) Google Scholar[4] L. V. Osipov, On large deviation probabilities for sums of independent random vectors, Theory Probab. Appl., 23 (1978), 490–506 10.1137/1123059 LinkGoogle Scholar[5] L. V. Osipov, Masters Thesis, Probabilities of Large Deviations for Sums of Independent Random Vectors, DSc Dissertation, Leningrad, 1978, (In Russian.) Google Scholar[6] V. J. Bentkus, Large deviations in Banach spaces, Theory Probab. Appl., 31 (1986), 627–632 10.1137/1131085 0657.60014 LinkGoogle Scholar[7] B. A. Zalessky, Probabilities of large deviations in Hilbert space, Theory Probab. Appl., 34 (1989), 650–655, (In Russian.) Google Scholar[8] V.-K. J. Bentkus, On large deviations in Banach spaces, 1st World Congress of Bernoulli Society, Abstracts of Commun., Vol. 2, Nauka, Moscow, 757– Google Scholar[9] V. J. Bentkus and , A. J. Račkauskas, On probabilities of large deviations in Banach spaces, Probab. Theory Related Fields, 86 (1990), 131–154 92a:60017 0678.60005 CrossrefGoogle Scholar[10] A. Račkauskas, Probabilities of large deviations in Linnik zones in a Hilbert space, Lith. Math. J., 28 (1988), 239–247 0714.60004 CrossrefGoogle Scholar[11] E. Bolthausen, Laplace approximations for sums of independent random vectors, Probab. Theory Relat. Fields, 72 (1986), 305–318 88b:60075 0572.60007 E. Bolthausen, Laplace approximations for sums of independent random vectors. II. Degenerate maxima and manifolds of maxima, Probab. Theory Related Fields, 76 (1987), 167–206 89g:60092 0608.60018 CrossrefGoogle Scholar[12] V. V. Yurinsky, On large deviation asymptotics in Hilbert space, 1988, Preprint No 23, Math. Inst. Siberian Division, USSR Academy Sci. Novosibirsk Google Scholar[13] F. Götze, Asymptotic expansions for bivariate von Mises functionals, Z. Wahrsch. Verw. Gebiete, 50 (1979), 333–355 81c:60025 0405.60009 CrossrefGoogle Scholar[14] V. V. Yurinsky, On the accuracy of normal approximation of the probability of hitting a ball, Theory Probab. Appl., 27 (1982), 280–289 10.1137/1127030 LinkGoogle Scholar[15] B. A. Zalesskii, , V. V. Sazonov and , V. V. Ul'yanov, Normal approximation in Hilbert space, I, Theory Probab. Appl., 33 (1988), 207–227 10.1137/1133037 B. A. Zalesskii, , V. V. Sazonov and , V. V. Ul'yanov, Normal approximation in Hilbert space, II, Theory Probab. Appl., 33 (1988), 473–487 10.1137/1133073 LinkGoogle Scholar[16] B. A. Zalesskii, , V. V. Sazonov and , V. V. Ul'yanov, A regular estimate of the accuracy of normal approximation in Hilbert space, Theory Probab. Appl., 33 (1988), 753–754 Google Scholar[17] R. N. Bhattacharya and , R. Ranga Rao, Normal approximation and asymptotic expansions, John Wiley & Sons, New York-London-Sydney, 1976xiv+274 55:9219 0331.41023 Google Scholar[18] V. V. Yurinsky, Exponential bounds for large deviations, Theory Probab. Appl., 19 (1974), 154–155 10.1137/1119012 LinkGoogle Scholar[19] V. V. Yurinsky, Exponential inequalities for sums of random vectors, J. Multivariate Anal., 6 (1976), 473–499 10.1016/0047-259X(76)90001-4 55:1422 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Precise Laplace-Type Asymptotics for Moderate Deviations of the Distributions of Sums of Independent Banach-Valued Random ElementsV. R. FatalovTheory of Probability & Its Applications, Vol. 48, No. 4 | 25 July 2006AbstractPDF (245 KB)Limit theorems for large deviations probabilities of certain quadratic formsLithuanian Mathematical Journal, Vol. 37, No. 4 | 1 Oct 1997 Cross Ref Nonuniform Exponential Estimates for Large Deviations in Banach SpaceI. R. Bagdasarova and E. I. OstrovskiiTheory of Probability & Its Applications, Vol. 40, No. 3 | 12 July 2006AbstractPDF (486 KB) Volume 36, Issue 1| 1992Theory of Probability & Its Applications1-208 History Submitted:31 May 1988Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1136008Article page range:pp. 99-114ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics