AN EXPONENTIAL NON-UNIFORM BERRY-ESSEEN BOUND OF SOME TIME INHOMOGENEOUS DIFFUSION PROCESS

doi:10.1007/s10473-025-0506-y

数学物理学报(英文版) ›› 2025, Vol. 45 ›› Issue (5): 1879-1890.doi: 10.1007/s10473-025-0506-y

AN EXPONENTIAL NON-UNIFORM BERRY-ESSEEN BOUND OF SOME TIME INHOMOGENEOUS DIFFUSION PROCESS

Qiaojing LIU¹, Yaqian LV², Baobin WANG^3,*

1. Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, China;
2. College of Mathematics and Physics, China Three Gorges University, Yichang 443002, China;
3. School of Mathematics and Statistics, South-Central MinZu University, Wuhan 430074, China

收稿日期:2024-06-06 修回日期:2025-02-13 出版日期:2025-09-25 发布日期:2025-10-14

AN EXPONENTIAL NON-UNIFORM BERRY-ESSEEN BOUND OF SOME TIME INHOMOGENEOUS DIFFUSION PROCESS

Qiaojing LIU¹, Yaqian LV², Baobin WANG^3,*

1. Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, China;
2. College of Mathematics and Physics, China Three Gorges University, Yichang 443002, China;
3. School of Mathematics and Statistics, South-Central MinZu University, Wuhan 430074, China

Received:2024-06-06 Revised:2025-02-13 Online:2025-09-25 Published:2025-10-14
Contact: ^*Baobin Wang, E-mail: wbb1818@126.com
About author:Qiaojing liu, E-mail: qjliu2002@163.com; Yaqian lv, E-mail: yaqian0408@163.com
Supported by:
This research was supported by the NSFC (12101358, 12471095), the Natural Science Foundation of Hubei Province in China (2024AFC020) and the Fundamental Research Funds for the Central Universities, South-Central MinZu University (CZY23010).

摘要/Abstract

摘要： In this paper, we study the exponential non-uniform Berry-Esseen bound for the maximum likelihood estimator of some time inhomogeneous diffusion process. As applications, the optimal uniform Berry-Esseen bound and optimal Cramér-type moderate deviations of the Ornstein-Uhlenbeck process and $\alpha$-Brownian bridge can be obtained. The main methods are the change of measure method and asymptotic analysis technique.

关键词: Berry-Esseen bound, time inhomogeneous diffusion process, Cramér-type moderate deviations, Ornstein-Uhlenbeck process

Abstract: In this paper, we study the exponential non-uniform Berry-Esseen bound for the maximum likelihood estimator of some time inhomogeneous diffusion process. As applications, the optimal uniform Berry-Esseen bound and optimal Cramér-type moderate deviations of the Ornstein-Uhlenbeck process and $\alpha$-Brownian bridge can be obtained. The main methods are the change of measure method and asymptotic analysis technique.

Key words: Berry-Esseen bound, time inhomogeneous diffusion process, Cramér-type moderate deviations, Ornstein-Uhlenbeck process

中图分类号:

62F12

Qiaojing LIU, Yaqian LV, Baobin WANG. AN EXPONENTIAL NON-UNIFORM BERRY-ESSEEN BOUND OF SOME TIME INHOMOGENEOUS DIFFUSION PROCESS[J]. 数学物理学报(英文版), 2025, 45(5): 1879-1890.

Qiaojing LIU, Yaqian LV, Baobin WANG. AN EXPONENTIAL NON-UNIFORM BERRY-ESSEEN BOUND OF SOME TIME INHOMOGENEOUS DIFFUSION PROCESS[J]. Acta mathematica scientia,Series B, 2025, 45(5): 1879-1890.

参考文献

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AN EXPONENTIAL NON-UNIFORM BERRY-ESSEEN BOUND OF SOME TIME INHOMOGENEOUS DIFFUSION PROCESS

AN EXPONENTIAL NON-UNIFORM BERRY-ESSEEN BOUND OF SOME TIME INHOMOGENEOUS DIFFUSION PROCESS

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