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

David R. Ba\~nos; Frank Proske; Sindre Duedahl; Thilo Meyer-Brandis

arxiv: 1503.09019 · v1 · pith:JYZMGC2Nnew · submitted 2015-03-31 · 🧮 math.PR · math.FA

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

David R. Ba\~nos , Sindre Duedahl , Thilo Meyer-Brandis , Frank Proske This is my paper

classification 🧮 math.PR math.FA

keywords solutionsmalliavinconditiondifferentiabledriftintegrabilitystrongunder

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

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