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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

Type
Article accepté pour publication ou publié
Date
1999
Journal name
Journal of Applied Probability
Volume
36
Number
1
Publisher
Applied Probability Trust
Pages
60-77
Publication identifier
Metadata
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Author(s)
Pham, Huyen
Florens, Danielle
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 / Keywords
Large deviations; rate function; Ornstein-Uhlenbeck diffusion process; drift estimation