爆炸状态带线性漂移项 Ornstein-Uhlenbeck 过程的精细大偏差

数学物理学报 ›› 2026, Vol. 46 ›› Issue (1): 305-317.

爆炸状态带线性漂移项 Ornstein-Uhlenbeck 过程的精细大偏差

李沁文(), 赵守江^*()

三峡大学数理学院湖北宜昌 443002
三峡大学三峡数学研究中心湖北宜昌 443002

收稿日期:2025-01-21 修回日期:2025-04-21 出版日期:2026-02-26 发布日期:2026-01-19
通讯作者: 赵守江 E-mail:2943769958@qq.com;shjzhao@163.com
作者简介:李沁文, Email: 2943769958@qq.com
基金资助:
国家自然科学基金(11601267)

Sharp Large Deviations of the Non-Stationary Ornstein-Uhlenbeck Process with Linear Drift

Qinwen Li(), Shoujiang Zhao^*()

School of Mathematics and Physics, China Three Gorges University, Hubei Yichang 443002
Three Gorges Mathematical Research Center, China Three Gorges University, Hubei Yichang 443002

Received:2025-01-21 Revised:2025-04-21 Online:2026-02-26 Published:2026-01-19
Contact: Shoujiang Zhao E-mail:2943769958@qq.com;shjzhao@163.com
Supported by:
NSFC(11601267)

摘要/Abstract

摘要：

Ornstein-Uhlenbeck (O-U) 过程作为一种重要的扩散过程, 在统计学、金融学、物理学等领域起重要作用. 该文利用测度变换技巧, 研究爆炸状态下带线性漂移项 O-U 过程的精细大偏差, 给出了极大似然估计尾概率的精细刻画. 作为应用得到了大偏差原理, 结果表明爆炸状态下有无线性漂移项 O-U 过程的极大似然估计具有相同的大偏差原理.

关键词: Ornstein-Uhlenbeck 过程, 极大似然估计, 精细大偏差

Abstract:

The Ornstein-Uhlenbeck (O-U) process, as an important diffusion process, plays a significant role in fields such as statistics, finance, and physics. In this paper, the sharp large deviations of the maximum likelihood estimation for the O-U process with linear drift in the explosive cases are studied by change of measure, and a refined characterization of the tail probability is obtained. As an application, the large deviation principle is obtained. The results demonstrate that the maximum likelihood estimations of the O-U process with and without linear drift in the explosive cases have the same large deviations.

Key words: Ornstein-Uhlenbeck process, maximum likelihood estimation, sharp large deviations

中图分类号:

O211.4

李沁文, 赵守江. 爆炸状态带线性漂移项 Ornstein-Uhlenbeck 过程的精细大偏差[J]. 数学物理学报, 2026, 46(1): 305-317.

Qinwen Li, Shoujiang Zhao. Sharp Large Deviations of the Non-Stationary Ornstein-Uhlenbeck Process with Linear Drift[J]. Acta mathematica scientia,Series A, 2026, 46(1): 305-317.

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