Stochastic differential equations | Vidéo | Carmin.tv

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Stochastic differential equations

By Gunther Leobacher

Appears in collection : Jean-Morlet Chair 2020 - Research School: Quasi-Monte Carlo Methods and Applications / Chaire Jean-Morlet 2020 - Ecole: Méthode de quasi-Monte-Carlo et applications

In the second part we show how the classical result can be used also for SDEs with drift that may be discontinuous and diffusion that may be degenerate. In that context I will present a concept of (multidimensional) piecewise Lipschitz drift where the set of discontinuities is a sufficiently smooth hypersurface in the multi-dimensional euclidean space. We discuss geometric properties of the set of discontinuities that are needed to transfer the convergence result from the Lipschitz case to the piecewise Lipschitz case.

Information about the video

Date of recording 02/11/2020
Date of publication 02/11/2020
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19680203
Cite this video Leobacher, Gunther (02/11/2020). Stochastic differential equations. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19680203
URL https://dx.doi.org/10.24350/CIRM.V.19680203

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Bibliography

Drmota, M.; Tichy, R.F.: Sequences, discrepancies and applications. Lecture Notes in Mathematics, 1651. Springer-Verlag, Berlin, 1997. - http://dx.doi.org/10.1007/BFb0093404
Kuipers, L.; Niederreiter, H.: Uniform distribution of sequences. Pure and Applied Mathematics. Wiley-Interscience, 1974.
Leobacher, G.; Pillichshammer, F.: Introduction to quasi-Monte Carlo integration and applications. Compact Textbooks in Mathematics. Birkhäuser, Cham, 2014. - http://dx.doi.org/10.1007/978-3-319-03425-6
Leobacher, Gunther; Szölgyenyi, Michaela A strong order 1/2 method for multidimensional SDEs with discontinuous drift.The Annals of Applied Probability, 2017, vol. 27, no 4, p. 2383-2418. - http://dx.doi.org/10.1214/16-AAP1262
Mao, X.: Stochastic differential equations and their applications. Series in Mathematics & Applications. Horwood Publishing Limited, Chichester, 1997 -

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