Sharp large deviations for the non-stationary Ornstein-Uhlenbeck process

被引：18

作者：

Bercu, Bernard ^{[1
]}

Coutin, Laure ^{[2
]}

Savy, Nicolas ^{[2
]}

机构：

[1] Univ Bordeaux 1, UMR C5251, Inst Math Bordeaux, F-33405 Talence, France

[2] Univ Toulouse 3, Inst Math Toulouse, UMR C5583, F-31062 Toulouse 09, France

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2012年 / 122卷 / 10期

关键词：

Large deviations; Ornstein-Uhlenbeck process; Likelihood estimation;

D O I：

10.1016/j.spa.2012.06.006

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：

For the Ornstein-Uhlenbeck process, the asymptotic behavior of the maximum likelihood estimator of the drift parameter is totally different in the stable, unstable, and explosive cases. Notwithstanding this trichotomy, we investigate sharp large deviation principles for this estimator in the three situations. In the explosive case, we exhibit a very unusual rate function with a shaped flat valley and an abrupt discontinuity point at its minimum. (C) 2012 Elsevier B.V. All rights reserved.

引用

页码：3393 / 3424

页数：32

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