Sharp large deviations for the non-stationary Ornstein–Uhlenbeck process
AbstractFor 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Stochastic Processes and their Applications.
Volume (Year): 122 (2012)
Issue (Month): 10 ()
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description
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- Shimizu, Yasutaka, 2009. "Notes on drift estimation for certain non-recurrent diffusion processes from sampled data," Statistics & Probability Letters, Elsevier, vol. 79(20), pages 2200-2207, October.
- Dietz Hans M. & Kutoyants Yury A., 2003. "Parameter estimation for some non-recurrent solutions of SDE," Statistics & Risk Modeling, De Gruyter, vol. 21(1/2003), pages 29-46, January.
- Zani, Marguerite, 2002. "Large deviations for squared radial Ornstein-Uhlenbeck processes," Stochastic Processes and their Applications, Elsevier, vol. 102(1), pages 25-42, November.
- Zhao, Shoujiang & Zhou, Yanping, 2013. "Sharp large deviations for the log-likelihood ratio of an α-Brownian bridge," Statistics & Probability Letters, Elsevier, vol. 83(12), pages 2750-2758.
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