分式奥恩斯坦-乌伦贝克过程中参数估计的适度偏差与 $$H \ in (0,{1\over 2})$$

Pub Date : 2024-04-19 DOI:10.1007/s10255-024-1083-x

Hui Jiang, Qing-shan Yang

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引用次数: 0

摘要

本文研究了具有赫斯特指数（H \in (0,{1 \over 2})\）的遍历分数奥恩斯坦-乌伦贝克过程中漂移函数中两个参数的估计值的渐近性质。可以得到克拉梅尔型温和偏差以及具有明确速率函数的温和偏差。主要方法包括多重维纳-伊托积分的偏差不等式和克拉梅尔型温和偏差，以及渐近分析技术。

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Moderate Deviations for the Parameter Estimation in the Fractional Ornstein-Uhlenbeck Process with $$H \in (0,{1 \over 2})$$

In this paper, we study the asymptotic properties for estimators of two parameters in the drift function in the ergodic fractional Ornstein-Uhlenbeck process with Hurst index $H \in (0,{1 \over 2})$. The Cramér-type moderate deviations, as well as the moderation deviations with explicit rate function can be obtained. The main methods consist of the deviation inequalities and Cramér-type moderate deviations for multiple Wiener-Itô integrals, as well as the asymptotic analysis techniques.

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