Some Estimates for Probabilities of One-Sided Large Deviations

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Previous article Next article Some Estimates for Probabilities of One-Sided Large DeviationsL. V. RozovskiiL. V. Rozovskiihttps://doi.org/10.1137/1130108PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] N. N. Amosova, The rate of convergence in the one-sided law of large numbers, Litovsk. Mat. Sb., 16 (1976), 5–12, 231, (In Russian.) 54:8813 0345.60018 Google Scholar[2] M. U. Gafurov, On estimates of the convergence rate in the law of the iterated logarithm, Abstracts of Reports of the 4th Japanese-Soviet Symposium on Probability Theory and Mathematical Statistics, Vol. I, Metsniereba, Tbilisi, 1982, 213–214, (In Russian.) Google Scholar[3] M. U. Gafurov and , A. D. Slastnikov, On the distribution of the time of last exit, the excess and the number of crossings of a random walk over a curvilinear boundary, Dokl. Akad. Nauk SSSR, 257 (1981), 526–529, (In Russian.) 82d:60125 Google Scholar[4] T. Avery Davis, Convergence rates for the law of the iterated logarithm, Ann. Math. Statist., 39 (1968), 1479–1485 40:6626 0174.49902 CrossrefGoogle Scholar[5] B. F. Skovoroda, On the convergence rate in the law of the iterated logarithm, Manuscript deposited in the VINITI, No. 4706-4783. (In Russian.) Google Scholar[6] L. V. Rozovskii˘, Estimates of the rate of convergence in the weak law of large numbers, Litovsk. Mat. Sb., 20 (1980), 147–163, 211, (In Russian.) 83i:60030 0463.60029 Google Scholar[7] M. U. Gafurov and , V. I. Rotar', On the exit of a random walk from curvilinear boundary, Theory Prob. Appl., 28 (1983), 179–184 0531.60065 LinkGoogle Scholar[8] V. V. Petrov, Sums of independent random variables, Springer-Verlag, New York, 1975x+346 52:9335 0322.60042 CrossrefGoogle Scholar[9] I. F. Pinelis, Limit theorems on large deviations with Cramer's condition violated for sums of infinite-dimensional random variables, Manuscript deposited in the VINITI, No. 1674-1681. (In Russian.) Google Scholar[10] A. I. Martikainen, One-sided versions of the law of large numbers: strong law and convergence rate, Sixteenth All-union School-Colloquium on Probability Theory and Mathematical Statistics, Bakuriani, Feb. 26-Mar. 5, 1982, Summaries of Reports, izd-vo TGU, Tbilisi, 1982, 48–54, (In Russian.) Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Small Deviation Probabilities for Maximum of Partial SumsL. V. Rozovsky11 November 2010 | Theory of Probability & Its Applications, Vol. 54, No. 4AbstractPDF (156 KB) Volume 30, Issue 4| 1986Theory of Probability & Its Applications History Submitted:29 March 1984Published online:28 July 2006 InformationCopyright © 1986 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1130108Article page range:pp. 850-855ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics