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Large deviations for the Ornstein-Uhlenbeck process with shift

Abstract : 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 non-steepness 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 one 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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https://hal.archives-ouvertes.fr/hal-01023543
Contributor : Bernard Bercu <>
Submitted on : Monday, July 14, 2014 - 10:01:39 AM
Last modification on : Thursday, January 11, 2018 - 6:21:22 AM
Document(s) archivé(s) le : Thursday, November 20, 2014 - 6:11:16 PM

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Bernard Bercu, Adrien Richou. Large deviations for the Ornstein-Uhlenbeck process with shift. 2014. ⟨hal-01023543⟩

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