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“Skew-Brownian Motion” and Derived Processes

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1991

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Previous article Next article "Skew-Brownian Motion" and Derived ProcessesY. OuknineY. Oukninehttps://doi.org/10.1137/1135018PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] J. M. Harrison and , L. A. Shepp, On skew Brownian motion, Ann. Probab., 9 (1981), 309–313 82j:60144 0462.60076 CrossrefGoogle Scholar[2] G. L. Kulinich, On necessary and sufficient conditions for convergence of solutions to one-dimensional stochastic diffusion equations with a nonregular dependence of the coefficients on a parameter, Theory Probab. Appl., 27 (1982), 856–861 10.1137/1127096 0522.60059 LinkGoogle Scholar[3] G. L. Kulinich, Limit behavior of solutions of stochastic diffusion equations when the convergence of coefficients is non-reqular, Lecture Notes in Math., Vol. 1021, Springer-Verlag, New York, Berlin, 1982, 352–354 0529.60057 Google Scholar[4] J. F. Legall, Temps locaux et équations différentielles stochastiques, Lecture Notes in Math., Vol. 986, Springer-Verlag, New York, Berlin, 1982 Google Scholar[5] N. Okada, , T. Okada and , B. Gaveaux, Second order differential operators and Dirichlet integrals with singular coefficients, I. Functional calculus of one-dimensional operators, Preprint Google Scholar[6] N. Okada, Personal communication Google Scholar[7] N. I. Portenko, Generalized diffusion processes, Proceedings of the Third Japan-USSR Symposium on Probability Theory (Tashkent, 1975), Springer, Berlin, 1976, 500–523. Lecture Notes in Math., Vol. 550, New York 55:13587 0387.60086 Google Scholar[8] N. I. Portenko, Diffusion processes with generalized drift coefficients, Theory Probab. Appl., 24 (1979), 62–78 10.1137/1124005 0432.60094 LinkGoogle Scholar[9] J. Walsh, Diffusion with discontinuous local time (temps locaux), Astérisques, (1978), 52–53 Google Scholar[10] Shintaro Nakao, On the pathwise uniqueness of solutions of one-dimensional stochastic differential equations, Osaka J. Math., 9 (1972), 513–518 48:5182 0255.60039 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails An Ideal Class to Construct Solutions for Skew Brownian Motion EquationsJournal of Theoretical Probability, Vol. 35, No. 2 | 18 February 2021 Cross Ref Resolution of the skew Brownian motion equations with stochastic calculus for signed measuresStochastic Analysis and Applications, Vol. 39, No. 5 | 6 December 2020 Cross Ref A CLT for a class of stochastic integrals with application in statisticsLatin American Journal of Probability and Mathematical Statistics, Vol. 18, No. 1 | 1 Jan 2021 Cross Ref Journal of Interdisciplinary Mathematics, Vol. 24, No. 8 | 2021 Cross Ref Convergence rate of Euler scheme for time-inhomogeneous SDEs involving the local time of the unknown processStochastic Models, Vol. 36, No. 3 | 15 April 2020 Cross Ref On the semi-group of a scaled skew Bessel processStatistics & Probability Letters, Vol. 145 | 1 Feb 2019 Cross Ref A Convergence result for the Euler-Maruyama method of one-dimensional stochastic differential equations involving the local time of the unknown process at zero2018 International Conference on Electronics, Control, Optimization and Computer Science (ICECOCS) | 1 Dec 2018 Cross Ref Timing in the presence of directional predictability: optimal stopping of skew Brownian motionMathematical Methods of Operations Research, Vol. 86, No. 2 | 13 July 2017 Cross Ref EFFICIENT PIECEWISE TREES FOR THE GENERALIZED SKEW VASICEK MODEL WITH DISCONTINUOUS DRIFTInternational Journal of Theoretical and Applied Finance, Vol. 20, No. 04 | 24 May 2017 Cross Ref Multidimensional stochastic differential equations with distributional driftTransactions of the American Mathematical Society, Vol. 369, No. 3 | 20 June 2016 Cross Ref Exact Simulation of Brownian Diffusions with Drift Admitting JumpsDavid Dereudre, Sara Mazzonetto, and Sylvie RoellySIAM Journal on Scientific Computing, Vol. 39, No. 3 | 9 May 2017AbstractPDF (792 KB)Pathwise solvability of stochastic integral equations with generalized drift and non-smooth dispersion functionsAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques, Vol. 52, No. 2 | 1 May 2016 Cross Ref Continuity of Local Time: An Applied PerspectiveThe Fascination of Probability, Statistics and their Applications | 27 December 2015 Cross Ref Skew Disperson and Continuity of Local TimeJournal of Statistical Physics, Vol. 156, No. 2 | 16 May 2014 Cross Ref On the time inhomogeneous skew Brownian motionBulletin des Sciences Mathématiques, Vol. 137, No. 7 | 1 Oct 2013 Cross Ref Arbitrage in skew Brownian motion modelsInsurance: Mathematics and Economics, Vol. 50, No. 1 | 1 Jan 2012 Cross Ref Some parabolic PDEs whose drift is an irregular random noise in spaceThe Annals of Probability, Vol. 35, No. 6 | 1 Nov 2007 Cross Ref Skew Brownian Motion and Pricing European OptionsThe European Journal of Finance, Vol. 13, No. 6 | 1 Sep 2007 Cross Ref SELF EXCITING THRESHOLD INTEREST RATES MODELSInternational Journal of Theoretical and Applied Finance, Vol. 09, No. 07 | 21 November 2011 Cross Ref Asymmetric skew Bessel processes and their applications to financeJournal of Computational and Applied Mathematics, Vol. 186, No. 1 | 1 Feb 2006 Cross Ref A scheme for simulating one-dimensional diffusion processes with discontinuous coefficientsThe Annals of Applied Probability, Vol. 16, No. 1 | 1 Feb 2006 Cross Ref A note on some new perpetuitiesScandinavian Actuarial Journal, Vol. 2005, No. 4 | 1 Jul 2005 Cross Ref Self Exciting Threshold Interest Rates ModelsSSRN Electronic Journal | 1 Jan 2005 Cross Ref Volume 35, Issue 1| 1991Theory of Probability & Its Applications1-204 History Submitted:23 March 1987Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1135018Article page range:pp. 163-169ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics

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