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 .
Guangjun Shen. Xiuwei Yin. "Least Squares Estimation for -Fractional Bridge with Discrete Observations." Abstr. Appl. Anal. 2014 (SI35) 1 - 8, 2014. https://doi.org/10.1155/2014/748376