%0 Journal Article
%T 带线性自排斥漂移项的分数O-U过程的统计推断<br>Statistical Inference on the Fractional Ornstein-Uhlenbeck Process with the Linear Self-Repelling Drift
%A 杨晴
%A 闫理坦
%J Advances in Applied Mathematics
%P 2235-2254
%@ 2324-8009
%D 2023
%I Hans Publishing
%R 10.12677/AAM.2023.125229
%X 本文旨在利用最小二乘法研究带线性自排斥漂移项的分数O-U过程的统计推断。 假设B<sup>H</sup>=<img src=\"Edit_52656133-ab89-4642-84df-d5bd0602e501.png\" alt=\"\" />是Hurst 指数为<img src=\"Edit_97290d1f-cfc3-4502-8413-38111134da39.png\" alt=\"\" />的分数布朗运动，我们考虑下列方程，<img src=\"Edit_67a3177a-bc04-4058-b7a1-6300296e075e.png\" alt=\"\" />其中,<img src=\"Edit_b21677d1-6c77-47a2-8b8f-59727e2d7f4a.png\" alt=\"\" /> , θ &lt; 0 和σ, ν ∈ R 是三个参数。 这个过程是自吸引扩散的模拟(见Cranston and Le Jan, Math. Ann. 303 (1995), 87-93)，我们主要的目标是研究其参数的最小二乘估计。<br />
This dissertation aim is to study statistical inference on the fractional Ornstein- Uhlenbeck process with the linear self-attracting drift by least squares estimation. Let <span>B</span><sup>H</sup><span>=</span><img src=\"Edit_bc5e8c8a-e3fa-42b4-b532-fb0f5d281e9b.png\" alt=\"\" /> be a fractional Brownian motion with Hurst index <img src=\"Edit_7ecce7f9-019b-418b-ba8c-944978fd9c6e.png\" alt=\"\" /> .  We consider the following equation<img src=\"Edit_f9b52d7c-ad43-4353-9ee0-7d228ef3e26e.png\" alt=\"\" />, with <img src=\"Edit_848026c9-9a0d-4269-a715-fc4c94cba06e.png\" alt=\"\" />, where θ &lt; 0 and σ, ν ∈ R are three parameters. The process is an analogue of the self-attracting diffusion (Cranston and Le Jan, Math. Ann. 303 (1995), 87-93). Our main aim is to study the least squares estimations of its parameters.
%K 分数布朗运动，自排斥扩散，最小二乘估计<br>Fractional Brownian Motion
%K Self-Repelling Diffusions
%K Least Squares Estimation
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=65781