离散观测下高斯过程驱动的 Ornstein-Uhlenbeck 方程的参数估计

数学物理学报 ›› 2026, Vol. 46 ›› Issue (5): 2017-2029.

离散观测下高斯过程驱动的 Ornstein-Uhlenbeck 方程的参数估计

刘南南(), 陈晓鹏^*()

汕头大学数学系广东汕头 515821

收稿日期:2025-04-29 修回日期:2025-12-29 出版日期:2026-10-26 发布日期:2026-09-07
通讯作者: 陈晓鹏 E-mail:22nnliu@stu.edu.cn;xpchen@stu.edu.cn
作者简介:刘南南, E-mail: 22nnliu@stu.edu.cn
基金资助:
广东省自然科学基金面上项目(2025A1515011188);2025 年李嘉诚基金会 STU-GTIIT 联合研究项目(2025LKSFG02);广东省区域联合基金-地区培育项目(2023A1515140016)

Parameter Estimation for the Ornstein-Uhlenbeck Process Driven by Gaussian Process with Discrete Observations

Nannan Liu(), Xiaopeng Chen^*()

Department of Mathematics, Shantou University, Guangdong Shantou 515063

Received:2025-04-29 Revised:2025-12-29 Online:2026-10-26 Published:2026-09-07
Contact: Xiaopeng Chen E-mail:22nnliu@stu.edu.cn;xpchen@stu.edu.cn
Supported by:
Respective the Guangdong Natural Science Foundation(2025A1515011188);Li Ka Shing Foundation STU-GTIIT Joint-research Grant(2025LKSFG02);Guangdong-Dongguan Joint Research Fund(2023A1515140016)

摘要/Abstract

摘要：

Ornstein-Uhlenbeck 方程作为随机过程的一个重要模型, 在物理学、经济学和金融学等领域有着广泛的应用. 本文研究由高斯过程驱动的 Ornstein-Uhlenbeck 方程的参数估计问题, 基于离散观测数据, 采用矩估计法和最小二乘法构造漂移参数的估计量. 通过对该参数估计量的具体分析, 得到矩估计量和最小二乘估计量的一致性乃至强相合性, 并推导了一定条件下渐近分布的表达式.

关键词: Ornstein-Uhlenbeck 过程, 高斯过程, 一致性

Abstract:

The Ornstein-Uhlenbeck equation, serving as a significant model for stochastic processes, has a wide range of applications in many fields such as physics, economics, and finance. This paper investigates the parameter estimation problem for the Ornstein-Uhlenbeck equation driven by a Gaussian process. Based on discrete-time observations, we employ the method of moments and the least squares method to construct estimators for the drift parameter. Through a detailed theoretical analysis, we establish the consistency and even strong consistency of the proposed moment estimator and least squares estimator. Furthermore, the asymptotic distributions of these estimators are derived under suitable conditions.

Key words: Ornstein-Uhlenbeck process, Gaussian process, consistency

中图分类号:

O212.2

刘南南, 陈晓鹏. 离散观测下高斯过程驱动的 Ornstein-Uhlenbeck 方程的参数估计[J]. 数学物理学报, 2026, 46(5): 2017-2029.

Nannan Liu, Xiaopeng Chen. Parameter Estimation for the Ornstein-Uhlenbeck Process Driven by Gaussian Process with Discrete Observations[J]. Acta mathematica scientia,Series A, 2026, 46(5): 2017-2029.

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