Section: New Results
Stochastic Analysis
Participants : Nicolas Champagnat, Julien Claisse, Denis Talay.
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N. Champagnat studied in collaboration with P.-E. Jabin (Univ. of Maryland) strong existence and pathwise uniqueness for stochastic differential equations driven by a Brownian motion and with rough coefficients [34] . The method is an extension of the one of [50] , which studies well-posedness for deterministic dynamical system. Strong existence and pathwise uniqueness can be proved for example if the drift vector is
and the diffusion matrix is uniformly elliptic and with . This improves the previous conditions of [53] . -
J. Claisse and D. Talay studied in collaboration with X. Tan (Univ. of Paris Dauphine) a conditioning argument which is often used to prove the dynamic programming principle [36] . Their study of the literature revealed that previous proofs of this argument are incorrect or incomplete. They provided a rigorous and detailed proof by setting up martingale controlled problems in a original way.