Sharp large deviations for the non-stationary Ornstein-Uhlenbeck process

Bernard Bercu 1, 2 Laure Coutin 3 Nicolas Savy 3
2 ALEA - Advanced Learning Evolutionary Algorithms
Inria Bordeaux - Sud-Ouest, UB - Université de Bordeaux, CNRS - Centre National de la Recherche Scientifique : UMR5251
Abstract : For the Ornstein-Uhlenbeck process, the asymptotic behavior of the maximum likelihood estimator of the drift parameter is totally different in the stable, unstable, and explosive cases. Notwithstanding of this trichotomy, we investigate sharp large deviation principles for this estimator in the three situations. In the explosive case, we exhibit a very unusual rate function with a shaped flat valley and an abrupt discontinuity point at its minimum.
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Bernard Bercu, Laure Coutin, Nicolas Savy. Sharp large deviations for the non-stationary Ornstein-Uhlenbeck process. Stochastic Processes and their Applications, Elsevier, 2012, 122, pp.3393-3424. ⟨10.1016/j.spa.2012.06.006⟩. ⟨hal-00645074⟩

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