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Large deviations in estimation of an Ornstein-Uhlenbeck model

Part of: Limit theorems

Published online by Cambridge University Press:  14 July 2016

Danielle Florens-Landais  and
Huyên Pham
Danielle Florens-Landais*
Affiliation:
CEREMADE
Huyên Pham*
Affiliation:
Université de Marne-la-Vallée
*
∗Postal address: CEREMADE, 42 Rue de la Procession, 75015 Paris, France.
∗∗Postal address: Equipe d'Analyse et de Mathématiques Appliquées, Université de Marne la Vallée, Cité Descartes, 5 Boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée, Cedex 2, France. Email address: pham@math.univ-mlv.fr.
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Abstract

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.

Keywords

Large deviationsrate functionOrnstein–Uhlenbeck diffusion processdrift estimation

MSC classification

Secondary: 60F10: Large deviations
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 1 , March 1999 , pp. 60 - 77
Copyright
Copyright © Applied Probability Trust 1999 

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