%0 Journal Article
%T 由<i>α</i>-稳定过程驱动的线性自排斥扩散过程的渐近行为和参数估计<br>Asymptotic Behavior and Parameter Estimation of the Linear Self-Repelling Diffusion Driven by <i>α</i>-Stable Motion
%A 冯甜
%A 闫理坦
%J Statistics and Applications
%P 445-452
%@ 2325-226X
%D 2024
%I Hans Publishing
%R 10.12677/sa.2024.132044
%X 设<img src=\"https://html.hanspub.org/file/2581249-rId9.svg?20240424114555\" />为一维<img src=\"https://html.hanspub.org/file/2581249-rId11.svg?20240424114555\" />-稳定模型且<img src=\"https://html.hanspub.org/file/2581249-rId13.svg?20240424114555\" />。本文主要研究如下线性自排斥扩散的长时间行为和参数估计：<img src=\"https://html.hanspub.org/file/2581249-rId15.svg?20240424114555\" />，其中<img src=\"https://html.hanspub.org/file/2581249-rId17.svg?20240424114555\" />、<img src=\"https://html.hanspub.org/file/2581249-rId19.svg?20240424114555\" />是两个未知参数且<img src=\"https://html.hanspub.org/file/2581249-rId21.svg?20240424114555\" />。当<img src=\"https://html.hanspub.org/file/2581249-rId23.svg?20240424114555\" />且<i>t</i>趋于无穷大时，对任意<img src=\"https://html.hanspub.org/file/2581249-rId25.svg?20240424114555\" />，我们有<img src=\"https://html.hanspub.org/file/2581249-rId27.svg?20240424114555\" />和<img src=\"https://html.hanspub.org/file/2581249-rId29.svg?20240424114555\" />几乎处处成立，其中<img src=\"https://html.hanspub.org/file/2581249-rId31.svg?20240424114555\" />。在连续观测条件下，建立<img src=\"https://html.hanspub.org/file/2581249-rId33.svg?20240424114555\" />和<img src=\"https://html.hanspub.org/file/2581249-rId19.svg?20240424114555\" />的最小二乘估计讨论其相合性与渐近分布。 <br />
Let <img src=\"https://html.hanspub.org/file/2581249-rId36.svg?20240424114555\" /> be an <img src=\"https://html.hanspub.org/file/2581249-rId38.svg?20240424114555\" />-stable motion of one-dimension with <img src=\"https://html.hanspub.org/file/2581249-rId40.svg?20240424114555\" />. In this paper, we consider large time behaviors and parameter estimation of the linear self-repelling diffusion of the forms <img src=\"https://html.hanspub.org/file/2581249-rId42.svg?20240424114555\" /> where <img src=\"https://html.hanspub.org/file/2581249-rId44.svg?20240424114555\" /> and <img src=\"https://html.hanspub.org/file/2581249-rId46.svg?20240424114555\" /> are two unknown parameters. When <img src=\"https://html.hanspub.org/file/2581249-rId48.svg?20240424114555\" /> and <i>t</i> tends to infinity, we show that the convergence <img src=\"https://html.hanspub.org/file/2581249-rId50.svg?20240424114555\" /> and <img src=\"https://html.hanspub.org/file/2581249-rId52.svg?20240424114555\" /> hold almost surely for all <img src=\"https://html.hanspub.org/file/2581249-rId25.svg?20240424114555\" />, where <img src=\"https://html.hanspub.org/file/2581249-rId55.svg?20240424114555\" />. The least squares estimates of <img src=\"https://html.hanspub.org/file/2581249-rId57.svg?20240424114555\" /> and <img src=\"https://html.hanspub.org/file/2581249-rId59.svg?20240424114555\" /> are
%K 自排斥扩散，长时间行为，参数估计，渐近分布<br>Self-Repelling Diffusion
%K Large Time Behaviors
%K Parameter Estimation
%K Asymptotic Distribution
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=85123