Weak convergence of integral functionals of random walks weakly convergent to fractional Brownian motion

• Datum: 2007
• Hauptverfasser: Mishura, Yu. S., Rode, S. H., Мішура, Ю. С., Роде, С. Г.
• Format: Artikel
• Sprache: Ukrainisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2007
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/3368
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

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.