On the Distribution of the Maximum of Successive Partial Sums of Independent Random Variables

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Previous article Next article On the Distribution of the Maximum of Successive Partial Sums of Independent Random VariablesT. V. ArakT. V. Arakhttps://doi.org/10.1137/1119032PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] S. V. Nagaev, On the speed of convergence of the distribution of the maximum sums of independent random variables, Theory Prob. Applications, 15 (1970), 309–315 10.1137/1115036 0227.60017 LinkGoogle Scholar[2] V. B. Nevzorov, The distribution of the maximal sum of independent summands, Dokl. Akad. Nauk SSSR, 208 (1973), 43–45, (In Russian.) MR0315767 (47:4316) Google Scholar[3] T. V. Arak and , V. B. Nevzorov, Some estimates for the maximum cumulative sum of independent random variables, Theory Prob. Applications, 18 (1973), 384–387 10.1137/1118047 0322.60030 LinkGoogle Scholar[4] T. Arak, The rate of convergence of the distribution of the maximum of successive sums of independent random variables, Dokl. Akad. Nauk SSSR, 208 (1973), 11–13, (In Russian.) MR0319236 (47:7781) Google Scholar[5] A. Bikyalis, Estimates of the remainder term in the central limit theorem, Litovsk. Mat. Sb., 6 (1966), 323–346, (In Russian.) MR0210173 (35:1067) Google Scholar[6] I. I. Gikhman and , A. V. Skorokhod, Introduction to the theory of random processes, Translated from the Russian by Scripta Technica, Inc, W. B. Saunders Co., Philadelphia, Pa., 1969xiii+516 MR0247660 (40:923) Google Scholar[7] S. N. Bernshtein, Collected Works, Vol. 4, Publishing House “Nauka”, Moscow, 1964, (In Russian.) Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails First-passage times for random walks with nonidentically distributed incrementsThe Annals of Probability, Vol. 46, No. 6 Cross Ref Sharp probability estimates for random walks with barriers25 July 2008 | Probability Theory and Related Fields, Vol. 145, No. 1-2 Cross Ref Cramér Type Moderate deviations for the Maximum of Self-normalized SumsElectronic Journal of Probability, Vol. 14, No. none Cross Ref Equivalence of rates of convergence in the CLT between maximum partial sums and first passage times of random walksScandinavian Actuarial Journal, Vol. 1983, No. 2 Cross Ref Limit Theorems for the First Passage Time of a Certain LevelN. I. Migai and V. B. Nevzorov17 July 2006 | Theory of Probability & Its Applications, Vol. 21, No. 2AbstractPDF (362 KB) Volume 19, Issue 2| 1975Theory of Probability & Its Applications History Submitted:09 July 1973Published online:28 July 2006 InformationCopyright © 1975 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1119032Article page range:pp. 245-266ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics