Limits for weighted pp-variations and likewise functionals of fractional diffusions with drift

Let XtXt be the pathwise solution of a diffusion driven by a fractional Brownian motion BtH with Hurst constant H>1/2H>1/2 and diffusion coefficient σ(t,x)σ(t,x). Consider the successive increments of this solution, ΔXi=Xi/n−X(i−1)/nΔXi=Xi/n−X(i−1)/n. Using a cylinder approximation for the solution XtXt, our main result yields that if 1/2