Previous article Next article On the Probability of Exit from a Square-Root Boundary by the Norm of a Brownian MotionA. F. RonzhinA. F. Ronzhinhttps://doi.org/10.1137/1130017PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] D. Jaeschke, The asymptotic distribution of the supremum of the standardized empirical distribution function on subintervals, Ann. Statist., 7 (1979), 108–115 80g:62009 0398.62013 CrossrefGoogle Scholar[2] L. Yu. Vostrikova, Detection of a “disorder” in a Wiener Process, Theory Prob. Appl., 24 (1981), 317–362 Google Scholar[3] A. P. Germogenov and , A. F. Ronzhin, A sequential chi-square test, Theory Prob. Appl., 29 (1984), 397–403 0565.62059 LinkGoogle Scholar[4] M. Abramowitz and , M. Stegun, Handbook of mathematical functions, with formulas, graphs and mathematical tables, Edited by Milton Abramowitz and Irene A. Stegun. Fifth printing, with corrections. National Bureau of Standards Applied Mathematics Series, Vol. 55, National Bureau of Standards, Washington, D.C., (for sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 20402), 1966xiv+1046 34:8607 CrossrefGoogle Scholar[5] D. A. Darling and , P. Erdös, A limit theorem for the maximum of normalized sums of independent random variables, Duke Math. J., 23 (1956), 143–155 17,635c 0070.13806 CrossrefGoogle Scholar[6] I. I. Gikhman and , A. V. Skorokhod, Introduction to the Theory of Random Processes, Nauka, Moscow, 1977, (In Russian.) 0429.60002 Google Scholar[7] Leo Breiman, First exit times from a square root boundaryProc. Fifth Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66), Vol. II: Contributions to Probability Theory, Part 2, Univ. California Press, Berkeley, Calif., 1967, 9–16 35:3730 0241.60035 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Brownian motion in time-dependent logarithmic potential: Exact results for dynamics and first-passage propertiesThe Journal of Chemical Physics, Vol. 143, No. 11 Cross Ref Extremes of weighted Brownian Bridges in increasing dimension8 February 2012 | Extremes, Vol. 15, No. 4 Cross Ref Change-point analysis in increasing dimensionJournal of Multivariate Analysis, Vol. 111 Cross Ref Volume 30, Issue 1| 1986Theory of Probability & Its Applications History Submitted:28 May 1982Published online:28 July 2006 InformationCopyright © 1986 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1130017Article page range:pp. 160-162ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics