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

Authors
  • Shen, Guangjun1
  • Yan, Litan2
  • Cui, Jing1
  • 1 Anhui Normal University, Department of Mathematics, 1 East Beijing Rd., Wuhu, 241000, P.R. China , Wuhu (China)
  • 2 Donghua University, Department of Mathematics, 2999 North Renmin Rd., Songjiang, Shanghai, 201620, P.R. China , Songjiang, Shanghai (China)
Type
Published Article
Journal
Journal of Inequalities and Applications
Publisher
Springer International Publishing
Publication Date
Jun 03, 2013
Volume
2013
Issue
1
Identifiers
DOI: 10.1186/1029-242X-2013-275
Source
Springer Nature
Keywords
License
Green

Abstract

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. MSC:60F05, 60G15, 60H07.

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