Construction of Malliavin differentiable strong solutions of SDEs under an integrability condition on the drift without the Yamada-Watanabe principle

2015/03/31 by Baños, David R., Duedahl, Sindre, Meyer-Brandis, Thilo +1
#60H07 #60H10 #60H40 #60J60 #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR)

paper · doi:10.48550/arxiv.1503.09019

Abstract

In this paper we aim at employing a compactness criterion of Da Prato, Malliavin, Nualart for square integrable Brownian functionals to construct unique strong solutions of SDE's under an integrability condition on the drift coefficient. The obtained solutions turn out to be Malliavin differentiable and are used to derive a Bismut-Elworthy-Li formula for solutions of the Kolmogorov equation.

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