Malliavin and flow regularity of SDEs. Application to the study of densities and the stochastic transport equation

David Banos; Torstein Nilssen

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arXiv · 1410.0786

Malliavin and flow regularity of SDEs. Application to the study of densities and the stochastic transport equation

David Banos·Torstein Nilssen

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Abstract

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.

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David Banos, Torstein Nilssen. 2015-09-10. Malliavin and flow regularity of SDEs. Application to the study of densities and the stochastic transport equation. https://arxiv.org/abs/1410.0786

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