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Estimation non paramétrique pour les processus markoviens déterministes par morceaux

Romain Azaïs 1, 2
2 CQFD - Quality control and dynamic reliability
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : Piecewise-deterministic Markov processes (PDMP’s) have been introduced by M.H.A. Davis as a general family of non-diffusion stochastic models, involving deterministic motion punctuated by random jumps at random times. In this thesis, we propose and analyze nonparametric estimation methods for both the features governing the randomness of such a process. More precisely, we present estimators of the conditional density of the inter-jumping times and of the transition kernel for a PDMP observed within a long time interval. We establish some convergence results for both the proposed estimators. In addition, numerical simulations illustrate our theoretical results. Furthermore, we propose an estimator for the jump rate of a nonhomogeneous renewal process and a numerical approximation method based on optimal quantization for a semiparametric regression model.
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Romain Azaïs. Estimation non paramétrique pour les processus markoviens déterministes par morceaux. Mathématiques générales [math.GM]. Université Sciences et Technologies - Bordeaux I, 2013. Français. ⟨NNT : 2013BOR14796⟩. ⟨tel-00844395⟩

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