English
Stochastic differential equations
Virtualconference
Auteurs : Leobacher, Gunther (Auteur de la Conférence)
CIRM (Editeur )
60H10 - Stochastic ordinary differential equations
65C05 - Monte Carlo methods
91G60 - Numerical methods in mathematical finance
CIRM (Editeur )
Loading the player...
|
Résumé :
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.
Keywords : Quasi-Monte Carlo; stochastic differential equations; irregular coefficients
Codes MSC : Keywords : Quasi-Monte Carlo; stochastic differential equations; irregular coefficients
60H10 - Stochastic ordinary differential equations
65C05 - Monte Carlo methods
91G60 - Numerical methods in mathematical finance
|
Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 02/11/2020 Date de captation : 02/11/2020 Sous collection : Research School arXiv category : Probability ; Numerical Analysis Domaine : Numerical Analysis & Scientific Computing ; Probability & Statistics Format : MP4 (.mp4) - HD Durée : 00/50:16 Audience : Researchers Download : https://videos.cirm-math.fr/2020-10-29_Leobacher 2.mp4 
|
Informations sur la Rencontre
Nom de la rencontre : Jean-Morlet Chair 2020 - Research School: Quasi-Monte Carlo Methods and Applications / Chaire Jean-Morlet 2020 - Ecole: Méthode de quasi-Monte-Carlo et applicationsOrganisateurs de la rencontre : Rivat, Joël ; Thonhauser, Stefan ; Tichy, Robert Dates : 02/11/2020 - 07/11/2020 Année de la rencontre : 2020 URL Congrès : https://www.chairejeanmorlet.com/2255.html
Données de citation
DOI : 10.24350/CIRM.V.19680203Citer cette vidéo: Leobacher, Gunther (2020). Stochastic differential equations. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19680203 URI : http://dx.doi.org/10.24350/CIRM.V.19680203 |
Voir aussi
- [Virtualconference] PDMPs in risk theory and QMC integration III / Auteur de la Conférence Thonhauser, Stefan.
- [Virtualconference] On the estimation of conditional quantiles - lecture 3 / Auteur de la Conférence Maume-Deschamps, Véronique.
- [Virtualconference] On the estimation of conditional quantiles - lecture 2 / Auteur de la Conférence Maume-Deschamps, Véronique.
- [Virtualconference] Number sequences for simulation - lecture 2 / Auteur de la Conférence Ökten, Giray.
- [Virtualconference] PDMPs and Integrals PDMPs in risk theory and QMC integration II / Auteur de la Conférence Thonhauser, Stefan.
- [Virtualconference] Derivative pricing, simulation from non-uniform distributions - lecture 3 / Auteur de la Conférence Ökten, Giray.
- [Multi angle] Quasi-Monte Carlo methods and applications: introduction / Auteur de la Conférence Tichy, Robert.
- [Virtualconference] Risk theory: models and objectives PDMPs in risk theory and QMC integration I / Auteur de la Conférence Thonhauser, Stefan.
- [Virtualconference] The coordinate sampler: a non-reversible Gibbs-like MCMC sampler / Auteur de la Conférence Robert, Christian P.
- [Virtualconference] On the estimation of conditional quantiles - lecture 1 / Auteur de la Conférence Maume-Deschamps, Véronique.
- [Virtualconference] Brief introduction of Quasi-Monte Carlo Methods and their Applications / Auteur de la Conférence Leobacher, Gunther.
- [Virtualconference] Two concrete FinTech applications of QMC / Auteur de la Conférence Larcher, Gerhard.
- [Virtualconference] Number sequences for simulation - lecture 1 / Auteur de la Conférence Ökten, Giray.
- [Virtualconference] Optimizing dividends and limited capital injections via exponential approximations I / Auteur de la Conférence Avram, Florin.
Bibliographie
- 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 -
