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

David Ruiz Baños, Sindre Duedahl, Thilo Meyer-Brandis, and Frank Norbert Proske
2015
 

Abstract

In this paper we aim at employing a compactness criterion of Da Prato, Malliavin, Nualart [2] 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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@UNPUBLISHED{BanosEtAl2015a,
    author = {Ba{\~n}os, David Ruiz and Duedahl, Sindre and Meyer-Brandis, Thilo and Proske, Frank Norbert},
     title = {Construction of Malliavin differentiable strong solutions of SDEs under an integrability condition
              on the drift without the Yamada-Watanabe principle},
      year = {2015},
  abstract = {In this paper we aim at employing a compactness criterion of Da Prato, Malliavin, Nualart [2] 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.},
       url = {http://arxiv.org/abs/1503.09019}
}