Branching for PDEs | Vidéo | Carmin.tv

00:00:00 / 00:00:00

Branching for PDEs

By Xavier Warin

Appears in collections : Research School, CEMRACS - Summer school: Numerical methods for stochastic models: control, uncertainty quantification, mean-field / CEMRACS - École d'été : Méthodes numériques pour équations stochastiques : contrôle, incertitude, champ moyen

Branching methods have recently been developed to solve some PDEs. Starting from Mckean formulation, we give the initial branching method to solve the KPP equation. We then give a formulation to solve non linear equation with a non linearity polynomial in the value function u. The methodology is extended for general non linearities in the value function u. Then we develop the methodology to solve non linear equation with non linearities polynomial in u and Du with convergence results. At last we give some numerical schemes to solve the semi-linear case and even the full non linear case but currently without convergence results.

Information about the video

Date of recording 19/07/2017
Date of publication 31/07/2017
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19199103
Cite this video Warin, Xavier (19/07/2017). Branching for PDEs. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19199103
URL https://dx.doi.org/10.24350/CIRM.V.19199103

Domain(s)

Bibliography

Bouchard, B., Tan, X., Warin, X., & Zou, Y. (2017). Numerical approximation of BSDEs using local polynomial drivers and branching processes. <arXiv:1612.06790> - https://arxiv.org/abs/1612.06790
Debrabant, K., & Jakobsen, E.R. (2013). Semi-Lagrangian schemes for linear and fully non-linear diffusion equations. Mathematics of Computation, 82(283), 433-1462 - https://doi.org/10.1090/S0025-5718-2012-02632-9
Doumbia, M., Oudjane, N., & Warin, X. (2016). Unbiased Monte Carlo estimate of stochastic differential equations expectations. <arXiv:1601.03139> - https://arxiv.org/abs/1601.03139
Fahim, A., Touzi, N., & Warin, X. (2011). A probabilistic numerical method for fully nonlinear parabolic PDEs. The Annals of Applied Probability, 21(4), 1322-1364 - http://dx.doi.org/10.1214/10-AAP723
Gevret, H., Lelong, J., & Warin, X. (2016). STochastic OPTimization library in C++. - https://hal.archives-ouvertes.fr/hal-01361291
Henry-Labordere, P., Tan, X., & Touzi, N. (2015). Unbiased simulation of stochastic differential equations. <arXiv:1504.06107> - https://arxiv.org/abs/1504.06107
Henry-Labordere, P. (2012). Counterparty risk valuation: a marked branching diffusion approach. Preprint - http://dx.doi.org/10.2139/ssrn.1995503
McKean, H.P. (1975). Application of Brownian motion to the equation of Kolmogorov-Petrovskii- Piskunov. Communications on Pure and Applied Mathematics, 28, 323-331 - http://dx.doi.org/10.1002/cpa.3160280302
Warin, X. (2017). Variations on branching methods for non linear PDEs. <arXiv:1701.07660> - https://arxiv.org/abs/1701.07660
Warin, X. (2013). Some non monotone schemes for time dependent Hamilton-Jacobi-Bellman equations in stochastic control. <arXiv:1310.6121> - https://arxiv.org/abs/1310.6121

MSC codes

Document(s)

https://www.fime-lab.org/

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow

Copyright Carmin.tv 2025

Give feedback