Fractional Brownian Motion and Sheet as White Noise Functionals

In this short note, we show that it is more natural to look the fractional Brownian motion as functionals of the standard white noises, and the fractional white noise calculus developed by Hu and Øksendal follows directly from the classical white noise functional calculus. As examples we prove that the fractional Girsanov formula, the Itô type integrals and the fractional Black–Scholes formula are easy consequences of their classical counterparts. An extension to the fractional Brownian sheet is also briefly discussed.