Abstract and Applied Analysis
Volume 2012 (2012), Article ID 804942, 14 pages
Research Article

Remarks on Confidence Intervals for Self-Similarity Parameter of a Subfractional Brownian Motion

1Department of Mathematics, Nanjing Audit University, 86 West Yushan Road, Pukou, Nanjing 211815, China
2Department of Mathematics, Donghua University, 2999 North Renmin Road, Songjiang, Shanghai 201620, China
3Department of Epidemiology and Biostatistics, Nanjing Medical University, 140 Hanzhong Road, Gulou, Nanjing 210029, China
4Department of Statistics, Xiamen University, 422 South Siming Road, Siming, Xiamen 361005, China

Received 4 August 2011; Revised 11 October 2011; Accepted 28 October 2011

Academic Editor: Ljubisa Kocinac

Copyright © 2012 Junfeng Liu 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.


We first present two convergence results about the second-order quadratic variations of the subfractional Brownian motion: the first is a deterministic asymptotic expansion; the second is a central limit theorem. Next we combine these results and concentration inequalities to build confidence intervals for the self-similarity parameter associated with one-dimensional subfractional Brownian motion.