Weak convergence of integral functionals of random walks weakly convergent to fractional Brownian motion
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.
English version (Springer): Ukrainian Mathematical Journal 59 (2007), no. 8, pp 1155-1162.
Citation Example: Mishura Yu. S., Rode S. H. Weak convergence of integral functionals of random walks weakly convergent to fractional Brownian motion // Ukr. Mat. Zh. - 2007. - 59, № 8. - pp. 1040–1046.