On the Speed of Convergence in a Boundary Problem. I

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Next article On the Speed of Convergence in a Boundary Problem. IS. V. NagaevS. V. Nagaevhttps://doi.org/10.1137/1115026PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] A. Ya. Khinchin, Asymptotic Laws of Probability Theory, ONTI, Moscow, Leningrad, 1936, (In Russian.) Google Scholar[2] Yu. V. Prokhorov, Convergence of stochastic processes and limit theorem in probability theory, Theory Prob. Applications, 1 (1956), 157–214 10.1137/1101016 LinkGoogle Scholar[3] 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 MR0185620 0146.37701 Google Scholar[4] A. A. Borovkov and , V. S. Korolyuk, On the results of asymptotic analysis in problems with boundaries, Theory Prob. Applications, 10 (1965), 236–246 10.1137/1110028 0144.18608 LinkGoogle Scholar[5] S. V. Nagaev, Some limit theorems for large deviations, Theory Prob. Applications, 10 (1965), 214–235 10.1137/1110027 0144.18704 LinkGoogle Scholar[6] Walter A. Rosenkrantz, On rates of convergence for the invariance principle, Trans. Amer. Math. Soc., 129 (1967), 542–552 MR0215347 0201.50902 CrossrefGoogle Scholar[7] Frank Spitzer, A combinatorial lemma and its application to probability theory, Trans. Amer. Math. Soc., 82 (1956), 323–339 MR0079851 0071.13003 CrossrefGoogle Scholar[8] Bengt Rosén, On the asymptotic distribution of sums of independent indentically distributed random variables, Ark. Mat., 4 (1962), 323–332 (1962) MR0142135 0103.11902 CrossrefGoogle Scholar[9] B. V. Gnedenko and , A. N. Kolmogorov, Limit distributions for sums of independent random variables, Addison-Wesley Publishing Company, Inc., Cambridge, Mass., 1954ix+264 MR0062975 0056.36001 Google Scholar Next article FiguresRelatedReferencesCited byDetails BOUNDARY CROSSING PROBABILITIES FOR THE CUMULATIVE SAMPLE MEAN8 March 2017 | Probability in the Engineering and Informational Sciences, Vol. 32, No. 2 Cross Ref The Entropic Erdős-Kac Limit Theorem1 April 2014 | Journal of Theoretical Probability, Vol. 28, No. 4 Cross Ref Linear and Nonlinear Boundary Crossing Probabilities for Brownian Motion and Related Processes14 July 2016 | Journal of Applied Probability, Vol. 47, No. 04 Cross Ref Linear and Nonlinear Boundary Crossing Probabilities for Brownian Motion and Related Processes14 July 2016 | Journal of Applied Probability, Vol. 47, No. 4 Cross Ref Асимптотика вероятности невыхода за криволинейную границу траектории гауссовского случайного блужданияИзвестия Российской академии наук. Серия математическая, Vol. 73, No. 1 Cross Ref Mixing Limit Theorems of Maximum of Absolute Sums and their Convergence RatesJournal of Theoretical Probability, Vol. 18, No. 4 Cross Ref Transient Phenomena in a Random WalkA. A. Aleskeviciené25 July 2006 | Theory of Probability & Its Applications, Vol. 48, No. 1AbstractPDF (197 KB)Approximations of boundary crossing probabilities for a Brownian motion14 July 2016 | Journal of Applied Probability, Vol. 36, No. 4 Cross Ref Testing the functions defining a nonlinear autoregressive time seriesStochastic Processes and their Applications, Vol. 36, No. 1 Cross Ref A course on empirical processes15 November 2006 Cross Ref On the Probabilities of Large Deviations for the Maximum of Sums of Independent Random Variables. IIA. K. Aleshkyavichene28 July 2006 | Theory of Probability & Its Applications, Vol. 24, No. 2AbstractPDF (814 KB)On the Probabilities of Large Deviations for the Maximum of Sums of Independent Random VariablesA. K. Aleshkyavichene17 July 2006 | Theory of Probability & Its Applications, Vol. 24, No. 1AbstractPDF (929 KB)Local Limit Theorems for the Density Function of the Maximum of a Sum of Independent VariablesA. D. Aleshkyavichene28 July 2006 | Theory of Probability & Its Applications, Vol. 21, No. 3AbstractPDF (1060 KB)On the Speed of Convergence in a Boundary ProblemA. I. Sahanenko28 July 2006 | Theory of Probability & Its Applications, Vol. 19, No. 2AbstractPDF (382 KB)Local limit theorems for first-passage time through a barrierLithuanian Mathematical Journal, Vol. 15, No. 1 Cross Ref Speeds of metric probability convergenceZeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 22, No. 4 Cross Ref On the Speed of Convergence in a Boundary Problem. IIS. V. Nagaev17 July 2006 | Theory of Probability & Its Applications, Vol. 15, No. 3AbstractPDF (1340 KB) Volume 15, Issue 2| 1970Theory of Probability & Its Applications History Submitted:22 December 1968Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1115026Article page range:pp. 163-186ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics