Fractional Wick Itô Skorohod (fWIS) integrals for fBm of Hurst index H >1/2

In this chapter we introduce the definition of stochastic integral with respect to the fBmfor Hurst index 1/2 <H <1 by using the white noise analysis method. At this purpose we define the fractional white noiseand stochastic integral as an element in the fractional Hida distribution space.

To obtain a classical Itô formula, we need the stochastic integral to be an ordinary random variable. Hence the ø-derivative is introduced to handle the existence of the Wick product in L². Classical Itô type formulas are obtained and applications are discussed. The main references for this chapter are [32], [83] and [121].