On Stopping Times for a Wiener Process

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Previous article Next article On Stopping Times for a Wiener ProcessA. A. NovikovA. A. Novikovhttps://doi.org/10.1137/1116049PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] H. Bateman and , A. Erdélyi, Higher transcendental functions. Vol. II, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1953xvii+396 MR0058756 0052.29502 Google Scholar[2] I. I. Gikhman and , A. V. Skorokhod, Stochastic Differential Equations, Izd-vo “Naukova dumka”, Kiev, 1968, (In Russian.) Google Scholar[3] J. L. Doob, Stochastic processes, John Wiley & Sons Inc., New York, 1953viii+654 MR0058896 0053.26802 Google Scholar[4] Kiyoshi Itô and , Henry P. McKean, Jr., Diffusion processes and their sample paths, Die Grundlehren der Mathematischen Wissenschaften, Band 125, Academic Press Inc., Publishers, New York, 1965xvii+321 MR0199891 0127.09503 CrossrefGoogle Scholar[5] P. Warwick Millar, Martingale integrals, Trans. Amer. Math. Soc., 133 (1968), 145–166 MR0226721 0164.46603 CrossrefGoogle Scholar[6] L. A. Shepp, A first passage problem for the Wiener process, Ann. Math. Statist., 38 (1967), 1912–1914 MR0217879 0178.19402 CrossrefGoogle Scholar[7] A. A. Novikov, On moment inequalities for stochastic integrals, Theory Prob. Applications, 16 (1971), 538–541 10.1137/1116058 0246.60047 LinkGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Пересечение броуновским движением границы порядка квадратного корняТруды Математического института имени В. А. Стеклова, Vol. 316 | 19 April 2022 Cross Ref Crossing an Asymptotically Square-Root Boundary by the Brownian MotionProceedings of the Steklov Institute of Mathematics, Vol. 316, No. 1 | 27 April 2022 Cross Ref Obstacle Problems Generated by the Estimates of Square FunctionGeometric Aspects of Harmonic Analysis | 24 February 2021 Cross Ref The Bellman Function Technique in Harmonic Analysis16 July 2020 Cross Ref On the first hitting time density for a reducible diffusion processQuantitative Finance, Vol. 20, No. 5 | 19 February 2020 Cross Ref First exit times of harmonically trapped particles: a didactic reviewJournal of Physics A: Mathematical and Theoretical, Vol. 48, No. 1 | 9 December 2014 Cross Ref Remarks on moment inequalities and identities for martingalesStatistics & Probability Letters, Vol. 83, No. 4 | 1 Apr 2013 Cross Ref First passage time problems with applications to synchronization2012 IEEE International Conference on Communications (ICC) | 1 Jun 2012 Cross Ref The Skorokhod embedding problem and its offspringProbability Surveys, Vol. 1, No. none | 1 Jan 2004 Cross Ref PASSPORT OPTIONSMathematical Finance, Vol. 12, No. 4 | 1 Oct 2002 Cross Ref Solving non–linear optimal stopping problems by the method of time–changeStochastic Analysis and Applications, Vol. 18, No. 5 | 1 Jan 2000 Cross Ref Approximations of boundary crossing probabilities for a Brownian motionJournal of Applied Probability, Vol. 36, No. 4 | 14 July 2016 Cross Ref Sequential Testing for Several Signals in Gaussian White NoiseTheory of Probability & Its Applications, Vol. 28, No. 3 | 17 July 2006AbstractPDF (814 KB)On Brownian slow pointsZeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 64, No. 3 | 1 Sep 1983 Cross Ref Semi-martingale inequalities via the Garsia-Rodemich-Rumsey lemma, and applications to local timesJournal of Functional Analysis, Vol. 49, No. 2 | 1 Nov 1982 Cross Ref On Discontinuous MartingalesTheory of Probability & Its Applications, Vol. 20, No. 1 | 17 July 2006AbstractPDF (1276 KB)On an Identity for Stochastic IntegralsTheory of Probability & Its Applications, Vol. 17, No. 4 | 28 July 2006AbstractPDF (413 KB)On Moment Inequalities for Stochastic IntegralsTheory of Probability & Its Applications, Vol. 16, No. 3 | 17 July 2006AbstractPDF (379 KB)A martingale approach to first passage problems and a new condition for Wald's identityStochastic Differential Systems Cross Ref Volume 16, Issue 3| 1971Theory of Probability & Its Applications401-574 History Submitted:13 June 1969Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1116049Article page range:pp. 449-456ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics