Abstract
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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 8, pp. 1040–1046, August, 2007.
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Mishura, Y.S., Rode, S.H. Weak convergence of integral functionals of random walks weakly convergent to fractional Brownian motion. Ukr Math J 59, 1155–1162 (2007). https://doi.org/10.1007/s11253-007-0077-1
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DOI: https://doi.org/10.1007/s11253-007-0077-1