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.

引用

页码：78 / 98

页数：21

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