Quasi-linear stochastic differential equations with a fractional Brownian component

The paper is devoted to stochastic differential equations with a fractional Brownian component. The fractional Brownian motion is constructed on the white noise space with the help of ``forward'' and ``backward'' fractional integrals. The fractional white noise and Wick products are considered. A similar construction for the ``complete'' fractional integral is considered by Elliott and van der Hoek. We consider two possible approaches to the existence and uniqueness of solutions of stochastic differential equation with a fractional Brownian motion.