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In this paper, using the recent results on Stein's method combining with Malliavin calculus and the almost sure central limit theorem for sequences of functionals of general Gaussian fields developed by Nourdin and Peccati, we derive the explicit bounds for the Kolmogorov distance in the central limit theorem and obtain the almost sure central limit theorem for the quadratic variation of the weighted fractional Brownian motion. © 2013 Shen et al.

Berry-Esséen bounds and almost sure CLT for quadratic variation of weighted fractional Brownian motion