Regularity properties of the stochastic flow of a skew fractional Brownian motion

Abstract

In this paper we prove, for small Hurst parameters, the higher-order differentiability of a stochastic flow associated with a stochastic differential equation driven by an additive multi-dimensional fractional Brownian noise, where the bounded variation part is given by the local time of the unknown solution process. The proof of this result relies on Fourier analysis-based variational calculus techniques and on intrinsic properties of the fractional Brownian motion.