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

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

2011-11-25

arxiv.org/abs/1111.6086v1

Mathematics

Probability

Scientific paper

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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