Observations bruitées d'une diffusion. Estimation, filtrage, applications.

Abstract : Diffusion models observed with noise are widely used in biology and in finance, to take into account an measurement error in the observation of a continuous-time stochastic process. Two statistical questions are relevant for these models : the estimation of a parameter $\theta$ of interest involved in the hidden diffusion, and the computation of the optimal filter, or an approximation. The first part of this thesis deals with a bidimensional Ornstein-Uhlenbeck model partially observed with noise, linked with the estimation of microvascularization parameters for a stochastic pharmacokinetic model. Results on medical data are presented. The second part is devoted to the estimation of the parameters of the hidden diffusion with high-frequency data, by minimization of contrast functions based on local means of noisy observations. Consistency and asymptotic normality are proved for these estimators. The last part deals with the tightness of the sequence of asymptotic variances obtained in the central limit theorem for the particle filter.
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Submitted on : Friday, October 8, 2010 - 10:57:47 AM
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Benjamin Favetto. Observations bruitées d'une diffusion. Estimation, filtrage, applications.. Mathematics [math]. Université René Descartes - Paris V, 2010. English. ⟨tel-00524565⟩

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