An Itô formula for generalized functionals of a fractional Brownian motion with arbitrary Hurst parameter

We consider fractional Brownian motions BtH with arbitrary Hurst coefficients 0<H<1 and prove the following results: (i) An integral representation of the fractional white noise as generalized Wiener integral; (ii) an Itô formula for generalized functionals of BtH; (iii) an analogue of Tanakaʹs formula; (iv) a Clark–Ocone formula for Donskerʹs delta function of BtH; (v) an integral representation of the local time of BtH.