WickItô Skorohod (WIS) integrals for fractional Brownian motion

In this chapter we again study the stochastic integral for the fBmfollowing the white noise approach. However, the integral is defined here as an element in the classicalHida distribution space by using the white noise theoryand Malliavin calculus for standard Brownian motionintroduced in Appendix A. The main advantage of this method with respect to the one presented in Chapter 3 is that it permits to define the stochastic integral for any H∈(0,1). In addition, it doesn't require the introduction of the fractional white noise theory since it uses the well-established one for the standard case.

On the other side, the approach of Chapter 3 can be seen as more intrinsic. For a further discussion of the relation among these two types of integrals we refer to Chapter 6. The main references for this chapter are [34] and [89].