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Malliavin and flow regularity of SDEs. Application to the study of densities and the stochastic transport equation. (English) Zbl 1337.60115
Summary: In this work, we present a condition for the regularity, in both space and Malliavin sense, of strong solutions to SDEs driven by Brownian motion. We conjecture that this condition is optimal. As a consequence, we are able to improve the regularity of densities of such solutions. We also apply these results to construct a classical solution to the stochastic transport equation when the drift is Lipschitz.

MSC:
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H07 Stochastic calculus of variations and the Malliavin calculus
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60J65 Brownian motion
60H40 White noise theory
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