LARGE DEVIATIONS AND CONCENTRATION INEQUALITIES FOR THE ORNSTEIN-UHLENBECK PROCESS WITHOUT TEARS

Abstract : Our goal is to establish large deviations and concentration inequalities 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. Notwithstanding of this trichotomy, we also provide new concentration inequalities for the maximum likelihood estimator.
Type de document :
Pré-publication, Document de travail
2016
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https://hal.archives-ouvertes.fr/hal-01270164
Contributeur : Adrien Richou <>
Soumis le : vendredi 5 février 2016 - 17:37:48
Dernière modification le : samedi 6 février 2016 - 01:07:21
Document(s) archivé(s) le : samedi 12 novembre 2016 - 12:28:09

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Bernard Bercu, Adrien Richou. LARGE DEVIATIONS AND CONCENTRATION INEQUALITIES FOR THE ORNSTEIN-UHLENBECK PROCESS WITHOUT TEARS. 2016. <hal-01270164>

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