September 2015 Large deviations for the Ornstein-Uhlenbeck process with shift
Bernard Bercu, Adrien Richou
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Adv. in Appl. Probab. 47(3): 880-901 (September 2015). DOI: 10.1239/aap/1444308886


We investigate the large deviation properties of the maximum likelihood estimators for the Ornstein-Uhlenbeck process with shift. We propose a new approach to establish large deviation principles which allows us, via a suitable transformation, to circumvent the classical nonsteepness problem. We estimate simultaneously the drift and shift parameters. On the one hand, we prove a large deviation principle for the maximum likelihood estimates of the drift and shift parameters. Surprisingly, we find that the drift estimator shares the same large deviation principle as the estimator previously established for the Ornstein-Uhlenbeck process without shift. Sharp large deviation principles are also provided. On the other hand, we show that the maximum likelihood estimator of the shift parameter satisfies a large deviation principle with a very unusual implicit rate function.


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Bernard Bercu. Adrien Richou. "Large deviations for the Ornstein-Uhlenbeck process with shift." Adv. in Appl. Probab. 47 (3) 880 - 901, September 2015.


Published: September 2015
First available in Project Euclid: 8 October 2015

zbMATH: 1326.60031
MathSciNet: MR3406612
Digital Object Identifier: 10.1239/aap/1444308886

Primary: 60F10 , 60G15 , 62F12

Keywords: large deviation , maximum likelihood estimate , Ornstein-Uhlenbeck process with shift

Rights: Copyright © 2015 Applied Probability Trust


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Vol.47 • No. 3 • September 2015
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