Stochastic stratonovich calculus fBm for fractional Brownian motion with hurst parameter less than 1/2

Abstract

In this paper we introduce a Stratonovich type stochastic integral with respect to the fractional Brownian motion with Hurst parameter less than 1/2. Using the techniques of the Malliavin calculus, we provide sufficient conditions for a process to be integrable. We deduce an Itô formula and we apply these results to study stochastic differential equations driven by a fractional Brownian motion with Hurst parameter less than 1/2.