Parameter Estimation for Ornstein-Uhlenbeck Driven by Ornstein-Uhlenbeck Processes with Small Levy Noises

被引：3
|
作者：
Zhang, Xuekang [1 ,2 ,3 ]
Shu, Huisheng [4 ]
Yi, Haoran [3 ]
机构：
[1] Anhui Polytech Univ, Sch Math Phys & Finance, Anhui Prov Dept Educ, Wuhu 241000, Peoples R China
[2] Anhui Polytech Univ, Energy Internet Engn Res Ctr, Wuhu 241000, Peoples R China
[3] Donghua Univ, Coll Informat Sci & Technol, Shanghai 201620, Peoples R China
[4] Donghua Univ, Coll Sci, Shanghai 201620, Peoples R China
来源：
JOURNAL OF THEORETICAL PROBABILITY | 2023年 / 36卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Ornstein-Uhlenbeck processes; Small Levy noises; Least squares estimator; Consistency; Asymptotic distribution; LEAST-SQUARES ESTIMATOR; STOCHASTIC DIFFERENTIAL-EQUATIONS;
D O I：
10.1007/s10959-022-01170-4
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
In this paper, we consider the problem of parameter estimation for Ornstein-Uhlenbeck driven by Ornstein-Uhlenbeck processes with small Levy noises, based on discrete observations at n regularly spaced time points t(i) = i/n, i = 1, 2, ..., n, on [0, 1]. Under certain conditions, we obtain the consistency and the rate of convergence of the least squares estimator when a small dispersion parameter epsilon tends to 0 and n -> infinity simultaneously. Additionally, the asymptotic distribution of the estimator is established.
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页码：78 / 98
页数：21
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