On the Rate of Convergence of Distributions of Functionals of Integral Type

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Previous article Next article On the Rate of Convergence of Distributions of Functionals of Integral TypeI. S. BorisovI. S. Borisovhttps://doi.org/10.1137/1121034PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Stanley Sawyer, Rates of convergence for some functionals in probability, Ann. Math. Statist., 43 (1972), 273–284 MR0301782 0239.60024 CrossrefGoogle Scholar[2] A. V. Skorokhod, Investigations in the Theory of Random Processes, Izd. Kievsk. Un-ta, (1961), , (In Russian.) Google Scholar[3] A. A. Borovkov, Notes on inequalities for sums of independent random variables, Theory Prob. Applications, 17 (1972), 556–557 10.1137/1117068 0283.60054 LinkGoogle Scholar[4] S. V. Nagaev and , D. Kh. Fuk, Probability inequalities for sums of independent random variables, Theory Prob. Applications, 16 (1971), 643–660 10.1137/1116071 0259.60024 LinkGoogle Scholar[5] V. V. Petrov, Sums of independent random variables, Springer-Verlag, New York, 1975x+346 MR0388499 0322.60042 CrossrefGoogle Scholar[6] Michel Loève, Probability theory, Third edition, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1963xvi+685 MR0203748 Google Scholar[7] D. H. Fuk, Certain probabilistic inequalities for martingales, Sibirsk. Mat. Ž., 14 (1973), 185–193, 239, (In Russian.) MR0326835 Google Scholar[8] A. A. Borovkov, On the rate of convergence for the invariance principle, Theory Prob. Applications, 18 (1973), 207–225 10.1137/1118025 0323.60031 LinkGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails A Refinement of Asymptotics in the Prokhorov–Donsker Invariance Principle for Integral FunctionalsN. K. Bakirov12 July 2006 | Theory of Probability & Its Applications, Vol. 40, No. 4AbstractPDF (1887 KB)Convergence rates of moments and related functionals in the invariance principle in Banach spacesLithuanian Mathematical Journal, Vol. 31, No. 2 Cross Ref Summary of Reports Presented at Sessions of the Seminar on Probability Theory and Mathematical Statistics at the Institute of Mathematics of the Siberian Section of the USSR Academy of Sciences (September–December 1985)17 July 2006 | Theory of Probability & Its Applications, Vol. 32, No. 1AbstractPDF (420 KB)An accuracy of Gaussian approximation of sum distribution of independent random variables in Banach spaces19 September 2006 Cross Ref Second-Order Approximation of Random Polygonal Lines in the Donsker-Prokhorov Invariance PrincipleI. S. Borisov and A. A. Borovkov3 August 2006 | Theory of Probability & Its Applications, Vol. 31, No. 2AbstractPDF (1786 KB)The Fiber Method and Its Application to the Study of Functionals of Stochastic ProcessesM. A. Lifshits17 July 2006 | Theory of Probability & Its Applications, Vol. 27, No. 1AbstractPDF (1262 KB)On Conditions of Existence of Bounded Density for Additive Functionals on Some Random ProcessesI. S. Borisov28 July 2006 | Theory of Probability & Its Applications, Vol. 25, No. 3AbstractPDF (818 KB) Volume 21, Issue 2| 1977Theory of Probability & Its Applications History Submitted:27 December 1974Published online:17 July 2006 InformationCopyright © 1977 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1121034Article page range:pp. 283-299ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics