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

Acta mathematica scientia,Series A ›› 2026, Vol. 46 ›› Issue (1): 305-317.

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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)

Abstract

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

CLC Number:

O211.4

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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References 16

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

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