Strong solutions of SDE's with generalized drift and multidimensional fractional Brownian initial noise

David R. Baños; Salvador Ortiz-Latorre; Andrey Pilipenko; Frank Proske

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arXiv · 1705.01616

Strong solutions of SDE's with generalized drift and multidimensional fractional Brownian initial noise

David R. Baños·Salvador Ortiz-Latorre·Andrey Pilipenko·Frank Proske

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Abstract

In this paper we prove the existence of strong solutions to a SDE with a generalized drift driven by a multidimensional fractional Brownian motion for small Hurst parameters H<1/2. Here the generalized drift is given as the local time of the unknown solution process, which can be considered an extension of the concept of a skew Brownian motion to the case of fractional Brownian motion. Our approach for the construction of strong solutions is new and relies on techniques from Malliavin calculus combined with a "local time variational calculus" argument.

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David R. Baños, Salvador Ortiz-Latorre, Andrey Pilipenko, Frank Proske. 2017-05-03. Strong solutions of SDE's with generalized drift and multidimensional fractional Brownian initial noise. https://arxiv.org/abs/1705.01616

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