# Strong solutions to stochastic differential equations with rough coefficients

1 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
2 Probabilités et statistiques
IECL - Institut Élie Cartan de Lorraine
3 Dpt of Mathematics
CSCAMM - Center for Scientific Computation and Mathematical Modeling
Abstract : We study strong existence and pathwise uniqueness for stochastic differential equations in $\RR^d$ with rough coefficients, and without assuming uniform ellipticity for the diffusion matrix. Our approach relies on direct quantitative estimates on solutions to the SDE, assuming Sobolev bounds on the drift and diffusion coefficients, and $L^p$ bounds for the solution of the corresponding Fokker-Planck PDE, which can be proved separately. This allows a great flexibility regarding the method employed to obtain these last bounds. Hence we are able to obtain general criteria in various cases, including the uniformly elliptic case in any dimension, the one-dimensional case and the Langevin (kinetic) case.
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Article dans une revue
The Annals of Probability, The Institute of Mathematics Statistics, In press
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Littérature citée [33 références]

https://hal.inria.fr/hal-00799242
Contributeur : Nicolas Champagnat <>
Soumis le : mardi 22 septembre 2015 - 09:41:49
Dernière modification le : samedi 27 janvier 2018 - 01:31:37
Document(s) archivé(s) le : mardi 29 décembre 2015 - 06:55:04

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strong_solutions_v13.pdf
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• HAL Id : hal-00799242, version 2

### Citation

Nicolas Champagnat, Pierre-Emmanuel Jabin. Strong solutions to stochastic differential equations with rough coefficients. The Annals of Probability, The Institute of Mathematics Statistics, In press. 〈hal-00799242v2〉

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