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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Pré-publication, Document de travail
2014
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Contributeur : Bernard Bercu <>
Soumis le : lundi 14 juillet 2014 - 10:01:39
Dernière modification le : mercredi 16 juillet 2014 - 15:52:32
Document(s) archivé(s) le : jeudi 20 novembre 2014 - 18:11:16

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  • HAL Id : hal-01023543, version 1

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

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