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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 748376, 8 pages
http://dx.doi.org/10.1155/2014/748376
Research Article

Least Squares Estimation for -Fractional Bridge with Discrete Observations

Department of Mathematics, Anhui Normal University, Wuhu 241000, China

Received 15 November 2013; Accepted 7 December 2013; Published 23 January 2014

Academic Editor: Litan Yan

Copyright © 2014 Guangjun Shen and Xiuwei Yin. 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 consider a fractional bridge defined as , where is a fractional Brownian motion of Hurst parameter and parameter is unknown. We are interested in the problem of estimating the unknown parameter . Assume that the process is observed at discrete time , and denotes the length of the “observation window.” We construct a least squares estimator of which is consistent; namely, converges to in probability as .