An \(S\)-transform approach to integration with respect to a fractional Brownian motion
An elementary definition of the (Wick)-Itô integral is given with respect to a fractional Brownian motion using the expectation, the ordinary Lebesgue integral and the classical (simple) Wiener integral. The expectation of the fractional Itô integral under change of measure is calculated and a Girsanov theorem for the fractional Itô integral is proven (not only for fractional Brownian motion). An Itô formula for functionals of a fractional Wiener integral is derived.
scientific article; zbMATH DE number 2072447