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Abstract and Applied Analysis
Volume 2014, Article ID 635917, 14 pages
http://dx.doi.org/10.1155/2014/635917
Research Article

Nonparametric Regression with Subfractional Brownian Motion via Malliavin Calculus

School of Mathematics and Statistics, Nanjing Audit University, 86 West Yushan Road, Pukou, Nanjing 211815, China

Received 27 November 2013; Accepted 13 December 2013; Published 6 February 2014

Academic Editor: Litan Yan

Copyright © 2014 Yuquan Cang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the asymptotic behavior of the sequence as tends to infinity, where and are two independent subfractional Brownian motions with indices and , respectively. is a kernel function and the bandwidth parameter satisfies some hypotheses in terms of and . Its limiting distribution is a mixed normal law involving the local time of the sub-fractional Brownian motion . We mainly use the techniques of Malliavin calculus with respect to sub-fractional Brownian motion.