The Distribution of the Norm of a Stable Vector
Nataliya V. Smorodina, Mikhail Lifshits · Theory of Probability and Its Applications · 1990
Previous article Next article The Distribution of the Norm of a Stable VectorN. V. Smorodina and M. A. LifshitsN. V. Smorodina and M. A. Lifshitshttps://doi.org/10.1137/1134022PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] N. V. Smorodina, Differential calculus on configuration space and stable measures, I, Theory Probab. Appl., 33 (1988), 488–499 10.1137/1133074 0673.60013 LinkGoogle Scholar[2] V. Yu. Bentkus and , D. Pap, Distribution of the norm of a stable random vector of a Hilbert space, Lithuanian Math. J., 26 (1986), 114–120 0608.60007 CrossrefGoogle Scholar[3] D. Pap, Masters Thesis, Properties of the distribution function of the norm of stable vectors in Banach spaces, Comp. Dissertation for Cand.of Math.-Phys. Sciences, Institute of Math. and Cybern., Akad. Nauk Litovsk. SSR Vil'nyus, 1985, (In Russian.) Google Scholar[4] D. Pap, Density of the norm of stable vector in Hilbert space, IV International Vil'nyus Conference on Probability and Mathematical Statistics, Summary of Reports, Vol. 4, Institute of Math. and Cybern., Akad. Nauk Litovsk. SSR, Vil'nyus, 1985, 223– Google Scholar[5] V. Yu. Bentkus, The asymptotic behavior of the moments in the central limit theory in Banach space, Soviet Math. Dokl., 28 (1983), 309–311 0565.60006 Google Scholar[6] V. M. Gol'dshtein and , Yu. G. Reshetnyak, An Introduction to the Theory of Functions with Generalized Derivatives and Quasiconformal Mappings, Nauka, Moscow, 1983, (In Russian.) 0591.46021 Google Scholar[7] V. I. Paulauskas and , A. Rachkauskas, Infinitely divisible and stable laws in separable Banach spaces, II, Lithuanian Math. J., 20 (1980), 305–316 0479.60016 CrossrefGoogle Scholar[8] N. V. Smorodina, Smoothness conditions for the densities of distributions of functionals of random processes, IV International Vil'nyus Conference on Probability and Mathematical Statistics, Summary of Reports, Vol. 4, Institute of Math. and Cybern., Akad. Nauk Litovsk. SSR, Vil'nyus, 1985, 143–145, (In Russian.) Google Scholar[9] Werner Linde, Infinitely divisible and stable measures on Banach spaces, Teubner-Texte zur Mathematik [Teubner Texts in Mathematics], Vol. 58, BSB B. G. Teubner Verlagsgesellschaft, Leipzig, 1983, 201– 86h:60006 0526.28011 Google Scholar[10] V. M. Kruglov and , S. N. Antonov, Once more on the asymptotic behavior of infinitly divisible distributions in Banach space, Theory Probab. Appl., 29 (1984), 766–775 10.1137/1129101 LinkGoogle Scholar[11] Walter Rudin, Functional analysis, McGraw-Hill Book Co., New York, 1973xiii+397 51:1315 0253.46001 Google Scholar[12] N. N. Vakhaniya, , V. I. Tarieladze and , S. A. Chobanyan, Probability distributions on Banach spaces, Mathematics and its Applications (Soviet Series), Vol. 14, D. Reidel Publishing Co., Dordrecht, 1987xxvi+482, Boston, Lancaster 97k:60007 0698.60003 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails An Asymptotic Expansion of the Distribution of a Homogeneous Functional of a Strictly Stable VectorN. V. Smorodina25 July 2006 | Theory of Probability & Its Applications, Vol. 41, No. 1AbstractPDF (449 KB)The Gauss–Ostrogradsky Formula for the Space of ConfigurationsN. V. Smorodina17 July 2006 | Theory of Probability & Its Applications, Vol. 35, No. 4AbstractPDF (1394 KB) Volume 34, Issue 2| 1990Theory of Probability & Its Applications History Submitted:27 March 1986Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1134022Article page range:pp. 266-274ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics