On Estimates of the Rate of Convergence in the Invariance Principle for Banach Spaces

Previous article Next article On Estimates of the Rate of Convergence in the Invariance Principle for Banach SpacesA. A. Borovkov and A. I. SakhanenkoA. A. Borovkov and A. I. Sakhanenkohttps://doi.org/10.1137/1125087PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Yu. V. Prokhorov, Convergence of random processes and limit theorems of probability theory, Theory Prob. Appl., 1 (1956), 157–214 LinkGoogle Scholar[2] A. V. Skorokhod, Studies in the theory of random processes, Translated from the Russian by Scripta Technica, Inc, Addison-Wesley Publishing Co., Inc., Reading, Mass., 1965viii+199 32:3082b 0146.37701 Google Scholar[3] J. Komlos, , P. Major and , G. Tusnady, An approximation of partial sums of independent RV's, and the sample DF. II, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 34 (1976), 33–58 53:6697 0307.60045 CrossrefGoogle Scholar[4] A. A. Borovkov, Rate of convergence and large deviations in invariance principle, Proceedings of the International Congress of Mathematicians (Helsinki, 1978), Acad. Sci. Fennica, Helsinki, 1980, 725–731 81j:60044 0438.60002 Google Scholar[5] A. A. Borovkov and , A. I. Sakhanenko, On the rate of convergence in the invariance principle in arbitrary spaces, Abstr.12th Europ. Meet. Statist., Varna, 1979 Google Scholar[6] István Berkes and , Walter Philipp, Approximation theorems for independent and weakly dependent random vectors, Ann. Probab., 7 (1979), 29–54 80k:60008 0392.60024 CrossrefGoogle Scholar[7] A. A. Borovkov, On the rate of convergence for the invariance principle, Theory Prob. Appl., 18 (1973), 207–225 LinkGoogle Scholar[8] Kh.-S. Go, Gaussian measures in Banach spaces, Mir, Moscow, 1979, (In Russian.) Google Scholar[9] A. I. Sakhanenko, Estimates of the rate of convergence in the invariance principle, Dokl. Akad. Nauk SSSR, 219 (1974), 1076–1078, (In Russian.) 51:6932 Google Scholar[10] T. V. Arak, On an estimate of A. A. Borovkov, Theory Prob. Appl., 20 (1975), 372–373 LinkGoogle Scholar[11] V. V. Gorodetskii, On the rate of convergence for the multidimensional invariance principle, Theory Prob. Appl., 20 (1975), 631–638 LinkGoogle Scholar[12] V. V. Yurinskii, A smoothing inequality for estimates of the Lévy-Prokhorov distance, Theory Prob. AppL., 20 (1975), 1–10 LinkGoogle Scholar[13] D. Kh. Fuk, Certain probabilistic inequalities for martingales, Sibirsk. Mat. Ž., 14 (1973), 185–193, 239, (In Russian.) 48:5177 Google Scholar[14] V. V. Senatov, On some estimates of the rate of convergence in the central limit theorem in Hilbert space in weak metrics, Second Vil'nyus Conference on the Theory of Prob. and Math. Statistics, Summary of Reports, Vol. 2, Vil'nyus, 1977, 175–178 Google Scholar[15] V. V. Senatov, Some remarks on nonuniform estimates for the rate of convergence, Teor. Veroyatnost. i Primenen., 33 (1988), 573–577 90c:60020 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Точность сильной гауссовской аппроксимации для сумм независимых случайных векторовУспехи математических наук, Vol. 68, No. 4(412) Cross Ref Estimates for the rate of strong approximation in Hilbert space24 August 2011 | Siberian Mathematical Journal, Vol. 52, No. 4 Cross Ref Bounds for the Rate of Strong Approximation in the Multidimensional Invariance PrincipleF. Götze and A. Yu. Zaitsev27 February 2009 | Theory of Probability & Its Applications, Vol. 53, No. 1AbstractPDF (249 KB)Theorems of large deviations in the multivariate invariance principleJournal of Multivariate Analysis, Vol. 41, No. 2 Cross Ref Convergence rates of moments and related functionals in the invariance principle in Banach spacesLithuanian Mathematical Journal, Vol. 31, No. 2 Cross Ref A useful estimate in the multidimensional invariance principleProbability Theory and Related Fields, Vol. 76, No. 1 Cross Ref Estimates of the Lévy–Prokhorov Distance in the Multivariate Central Limit Theorem for Random Variables with Finite Exponential MomentsA. Yu. Zaitsev3 August 2006 | Theory of Probability & Its Applications, Vol. 31, No. 2AbstractPDF (1777 KB)Estimates for the probability of ruin starting with a large initial reserveInsurance: Mathematics and Economics, Vol. 5, No. 4 Cross Ref On the Convergence Rate in the Invariance PrincipleA. A. Borovkov17 July 2006 | Theory of Probability & Its Applications, Vol. 29, No. 3AbstractPDF (348 KB)Summary of Reports Presented at Sessions of the Probability and Statistics Seminar at the Leningrad Section at the V. A. Steklov Mathematical Institute of the USSR Academy of Sciences, February–December 198317 July 2006 | Theory of Probability & Its Applications, Vol. 29, No. 4AbstractPDF (1774 KB)Summary of Reports Presented at Sessions of the Probability and Mathematical Statistics Seminar at the Mathematics Institute of the Siberian Section of the USSR Academy of Sciences, February–May 198217 July 2006 | Theory of Probability & Its Applications, Vol. 28, No. 3AbstractPDF (814 KB)On the Rate of Convergence in the Invariance Principle for Generalized Renewal ProcessesK. A. Borovkov17 July 2006 | Theory of Probability & Its Applications, Vol. 27, No. 3AbstractPDF (727 KB) Volume 25, Issue 4| 1981Theory of Probability & Its Applications History Submitted:03 April 1980Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1125087Article page range:pp. 721-731ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics

Перевод пока недоступен