## Abstract and Applied Analysis

### Least Squares Estimation for $\alpha$-Fractional Bridge with Discrete Observations

#### Abstract

We consider a fractional bridge defined as $d{X}_{t}=-\alpha {\mathrm{(X}}_{t}/(T-t))dt+d{B}_{t}^{H}, \mathrm{0}\le t, where ${B}^{H}$ is a fractional Brownian motion of Hurst parameter $H>\mathrm{1}/\mathrm{2}$ and parameter $\alpha >\mathrm{0}$ is unknown. We are interested in the problem of estimating the unknown parameter $\alpha >\mathrm{0}$. Assume that the process is observed at discrete time ${t}_{i}=i{\Delta }_{n}, i=\mathrm{0},\dots ,n$, and ${T}_{n}=n{\Delta }_{n}$ denotes the length of the “observation window.” We construct a least squares estimator ${\stackrel{^}{\alpha }}_{n}$ of $\alpha$ which is consistent; namely, ${\stackrel{^}{\alpha }}_{n}$ converges to $\alpha$ in probability as $n\to \mathrm{\infty }$.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 748376, 8 pages.

Dates
First available in Project Euclid: 26 March 2014

https://projecteuclid.org/euclid.aaa/1395858396

Digital Object Identifier
doi:10.1155/2014/748376

Mathematical Reviews number (MathSciNet)
MR3166653

Zentralblatt MATH identifier
07023012

#### Citation

Shen, Guangjun; Yin, Xiuwei. Least Squares Estimation for $\alpha$ -Fractional Bridge with Discrete Observations. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 748376, 8 pages. doi:10.1155/2014/748376. https://projecteuclid.org/euclid.aaa/1395858396

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