Large deviations in estimation of an Ornstein-Uhlenbeck model
Pham, Huyen; Florens, Danielle (1999), Large deviations in estimation of an Ornstein-Uhlenbeck model, Journal of Applied Probability, 36, 1, p. 60-77. http://dx.doi.org/10.1239/jap/1032374229
TypeArticle accepté pour publication ou publié
Journal nameJournal of Applied Probability
Applied Probability Trust
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Abstract (EN)A large deviation principle (LDP) with an explicit rate function is proved for the estimation of drift parameter of the Ornstein-Uhlenbeck process. We establish an LDP for two estimating functions, one of them being the score function. The first one is derived by applying the Gärtner-Ellis theorem. But this theorem is not suitable for the LDP on the score function and we circumvent this key point by using a parameter-dependent change of measure. We then state large deviation principles for the maximum likelihood estimator and another consistent drift estimator.
Subjects / KeywordsLarge deviations; rate function; Ornstein-Uhlenbeck diffusion process; drift estimation
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