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

Bernard Bercu (1, 2) , Laure Coutin (3) , Nicolas Savy (3)

1 IMB - Institut de Mathématiques de Bordeaux
2 ALEA - Advanced Learning Evolutionary Algorithms
3 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Mots clés: Large deviations; Ornstein-Uhlenbeck process; Likelihood estimation

Domaines: Probabilités [math.PR]

Bernard Bercu, Laure Coutin, Nicolas Savy. Sharp large deviations for the non-stationary Ornstein-Uhlenbeck process. Stochastic Processes and their Applications, 2012, 122, pp.3393-3424. ⟨10.1016/j.spa.2012.06.006⟩. ⟨hal-00645074⟩