Weak convergence of integral functionals of random walks weakly convergent to fractional Brownian motion - Mishura, Yu. S.; Rode, S. H. (Ukrains’kyi Matematychnyi Zhurnal, 2007)
We consider a random walk that converges weakly to a fractional Brownian motion with Hurst index H > 1/2. We construct an integral-type functional of this random walk and prove that it converges weakly to an integral constructed on the basis of the fractional Brownian motion.