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Sharp large deviations for the non-stationary Ornstein-Uhlenbeck process. (English) Zbl 1316.60035
Summary: 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 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.

MSC:
60F10 Large deviations
60J60 Diffusion processes
62F12 Asymptotic properties of parametric estimators
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