Asymptotic behavior of maximum likelihood estimators for Ornstein-Uhlenbeck process with large linear drift

被引：0

作者：

Zhang, Xuekang ^{[1
,2
]}

机构：

[1] Anhui Polytech Univ, Sch Math Phys & Finance, Wuhu 241000, Peoples R China

[2] Anhui Polytech Univ, Key Lab Adv Percept & Intelligent Control High End, Minist Educ, Wuhu 241000, Peoples R China

来源：

STOCHASTICS AND DYNAMICS | 2023年 / 23卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Maximum likelihood estimators; Ornstein-Uhlenbeck process; large linear drift; law of iterated logarithm; consistency; asymptotic distributions; SHARP LARGE DEVIATIONS; PARAMETERS;

D O I：

10.1142/S0219493723500247

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 study the asymptotic behavior of maximum likelihood estimators for Ornstein-Uhlenbeck process with large linear drift dX(t) = -1/epsilon (theta X-t - epsilon(1/2) nu)dt + dB(t), 0 <= t <= T, where theta, nu is an element of R, and { B-t }(t >= 0) is a given standard Brownian motion. The law of iterated logarithm, consistency and asymptotic distributions of the estimators are discussed based on the continuous observation {X-t}(t is an element of[0,T]) as epsilon -> 0.

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页数：19

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