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Theses

Méthodes de lissage et d'estimation dans des modèles à variables latentes par des méthodes de Monte-Carlo séquentielles

Abstract : Hidden Markov chain models or more generally Feynman-Kac models are now widely used. They allow the modelling of a variety of time series (in finance, biology, signal processing, ...) Their increasing complexity gave birth to approximations using Monte-Carlo methods, among which Markov Chain Monte-Carlo (MCMC) and Sequential Monte-Carlo (SMC). SMC methods applied to particle filtering and smoothing are dealt with in this thesis. These methods consist in approximating the law of interest through a particle population sequentially defined. Different algorithms have already been developed and studied in the literature. We make some of these results more precise in the particular of the Forward Filtering Backward Smoothing and Forward Filtering Backward Simulation by showing exponential deviation inequalities and by giving non-asymptotic upper bounds to the mean error. We also introduce a new smoothing algorithm improving a particle population through MCMC iterations and allowing to estimate the estimator variance without further simulation. Part of the work presented in this thesis is devoted to the parallel computing of particle estimators. We study different interaction schemes between several particle populations. Finally, we also illustrate the use of hidden Markov chains in the modelling of financial data through an algorithm using Expectation-Maximization to calibrate the exponential Ornstein-Uhlenbeck multiscale stochastic volatility model
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Cyrille Dubarry. Méthodes de lissage et d'estimation dans des modèles à variables latentes par des méthodes de Monte-Carlo séquentielles. Mathématiques générales [math.GM]. Institut National des Télécommunications, 2012. Français. ⟨NNT : 2012TELE0040⟩. ⟨tel-00762243⟩

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