Asymptotic behavior of weighted quadratic variation of tempered fractional Brownian motion

Abstract

This paper investigates the convergence in L2 of renormalized weighted quadratic variation associated to tempered fractional Brownian motion with Hurst index 0 < H < 1/4 and λ>0. We first give four lemmas about tempered fractional Brownian motion by means of Malliavin calculus. Then the convergence for tempered fractional Brownian motion is derived in L2 through these lemmas. Our main result extends findings of Nourdin (2008), concerning the weighted power variations of fractional Brownian motion.