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

Bernard Bercu, Laure Coutin and Nicolas Savy

Stochastic Processes and their Applications, 2012, vol. 122, issue 10, 3393-3424

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 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.

Keywords: Large deviations; Ornstein–Uhlenbeck process; Likelihood estimation (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:122:y:2012:i:10:p:3393-3424

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DOI: 10.1016/j.spa.2012.06.006

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