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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