School of Mathematics and Statistics
Hunan University of Science and Technology
Xiangtan, Hunan 411201, China
email: knh1552@163.com
School of Mathematics and Statistics
Linyi University
Linyi, Shandong 276005, China
email: xiehuantian@lyu.edu.cn
Nenghui Kuang, Huantian Xie
Abstract:
In this article we consider least squares estimation (LSE) for sub-fractional Brownian
bridge with linear drift defined by
$$
dX_t=\frac{\alpha (k-X_t)}{T-t}dt+dS^{H}_t, \quad 0\leq t< T,\quad
X_0=x_0,
$$
where \(\alpha>0\), \(k\in R\) and \(\tau:=\alpha k\) are
unknown parameters, and \(S^{H}\) is a sub-fractional Brownian with Hurst index
\(H\in (1/2, 1)\). We prove that the LSE has strong consistency as
\(t\to T\) depending on the value of \(\alpha\). When it has consistency, we obtain the
rate of this convergence. This work extends the results by Kuang and Liu [11] who
studied the case \(k=0\) and \(x_0=0\).
Submitted September 25, 2025. Published June 11, 2026.
Math Subject Classifications: 60G15, 60H05, 62F12.
Key Words: Least squares estimation; sub-fractional Brownian bridge; strong consistency.
DOI: 10.58997/ejde.2026.41
Show me the PDF file (433 KB), TEX file for this article.
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Nenghui Kuang School of Mathematics and Statistics Hunan University of Science and Technology Xiangtan, Hunan 411201, China email: knh1552@163.com |
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Huantian Xie School of Mathematics and Statistics Linyi University Linyi, Shandong 276005, China email: xiehuantian@lyu.edu.cn |
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