Convergence de semi-groupes de diffusion : amplitude et problème de Skorokhod

Abstract : This thesis is divided in three independant parts. In first part is estimated the convergence rate of sorne semi-groups associated to diffusion processes to their invariant probability. Second part deals with the law of the range process for ultraspherical Markov chains and Bessel processes. Convergence of ultraspherical Markov chains to Bessel processes is first established. Then are evaluated Laplace transform and firts moment for the range inverse (firt passage time for the range process to a given level). Calculations are developped in the case of Bessel processes of dimension one and three. In third part are considered two classes of martingale: 1 - The class of right continuous left limited, uniformly integrable martingales, (Mt)t?0, such that the law of (M0, M?) is given. 2 - The class of right continuous left limited, uniformly intégrable martingales, (Mt)t?0 such that the laws of M0 and M? are given. For each of these two kind of Skorokhod's problem, we construct an explicit brownian solution. These solutions are of great importance in maximal inequalies.
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Theses
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http://docnum.univ-lorraine.fr/prive/SCD_T_1999_0279_GANIDIS_COCHARD.pdf
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Hélène Ganidis-Cochard. Convergence de semi-groupes de diffusion : amplitude et problème de Skorokhod. Mathématiques générales [math.GM]. Université Henri Poincaré - Nancy 1, 1999. Français. ⟨NNT : 1999NAN10279⟩. ⟨tel-01747285⟩

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