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

Abstract

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

CLC Number:

O212.2

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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References 31

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

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