Asymptotic normality in partially observed diffusions with small noise: application to FDI

François Le Gland 1 Bo Wang 1
1 SIGMA2 - Signal, models, algorithms
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, INRIA Rennes
Abstract : The problem of residual evaluation for fault detection in partially observed diffusions is investigated, using the local asymptotic approach, under the small noise asymptotics. The score function (i.e. the gradient of the log-likelihood function) evaluated at the nominal value of the parameter, and suitably normalized, is used as residual. It is proved that this residual is asymptotically Gaussian, with mean zero under the null hypothesis, with a different mean (depending linearly on the parameter change) and the same covariance matrix under the contiguous alternative hypothesis. This result relies on the local asymptotic normality (LAN) property for the family of probability distributions of the observation process, which is also proved.
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Chapitre d'ouvrage
Pasik―Duncan, Boženna. Stochastic Theory and Control, Lawrence 2001. In honor of Tyrone E. Duncan on the occasion of his 60th birthday, 280, Springer, pp.267-282, 2002, Lecture Notes in Control and Information Sciences, 〈10.1007/3-540-48022-6_19〉
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https://hal.inria.fr/hal-00912084
Contributeur : Francois Le Gland <>
Soumis le : dimanche 1 décembre 2013 - 23:25:51
Dernière modification le : mercredi 16 mai 2018 - 11:23:05

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François Le Gland, Bo Wang. Asymptotic normality in partially observed diffusions with small noise: application to FDI. Pasik―Duncan, Boženna. Stochastic Theory and Control, Lawrence 2001. In honor of Tyrone E. Duncan on the occasion of his 60th birthday, 280, Springer, pp.267-282, 2002, Lecture Notes in Control and Information Sciences, 〈10.1007/3-540-48022-6_19〉. 〈hal-00912084〉

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