Large deviations for the Ornstein-Uhlenbeck process without tears

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• 作者：Bernard Bercu ; ^{bernard.bercu@u-bordeaux.fr} ; Adrien Richou ^{adrien.richou@u-bordeaux.fr}
• 关键词：Ornstein&ndash ; Uhlenbeck process ; Maximum likelihood estimates ; Large deviations
• 刊名：Statistics & Probability Letters
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：123
• 期：Complete
• 页码：45-55
• 全文大小：434 K
• 卷排序：123

文摘

Our goal is to establish large deviations for the maximum likelihood estimator of the drift parameter of the Ornstein–Uhlenbeck process without tears. We propose a new strategy to establish large deviation results which allows us, via a suitable transformation, to circumvent the classical difficulty of non-steepness. Our approach holds in the stable case where the process is positive recurrent as well as in the unstable and explosive cases where the process is respectively null recurrent and transient. It can also be successfully implemented for more complex diffusion processes.