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 integralwith respect to the fractional Brownian motion with Hurst parameter less than1/2. Using the techniques of the Malliavin calculus, we provide sufficientconditions for a process to be integrable. We deduce an It^o formula andwe apply these results to study stochastic differential equations driven by afractional Brownian motion with Hurst parameter less than 1/2.