Strong Solutions of Stochastic Differential Equations with Generalized Drift and Multidimensional Fractional Brownian Initial Noise
- Banos, David
- Ortiz-Latorre, Salvador
- Pilipenko, Andrey
Publication date
January 2021
DOI Publisher
Springer Science and Business Media LLCAbstract
In this paper, we prove the existence of strong solutions to an stochastic differential equation with a generalized drift driven by a multidimensional fractional Brownian motion for small Hurst parameters H<12. 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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