Strong solutions of SDE's with generalized drift and multidimensional fractional Brownian initial noise
arXiv:1705.01616
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.
45 pages. arXiv admin note: text overlap with arXiv:1511.02717