Processus associés à l'équation de diffusion rapide : étude asymptotique du temps de ruine et de l'overshoot

Abstract : I- Processes of Rapid Diffusion. We check the existence and the unicity of the process associated with the equation of rapid diffusion for a large class of initial data. We show the convergence to the solution associated with the Dirac measure at 0. II- Ruin and Overshoot : Asymptotic Behaviour. Let Tx be the first hitting time of level x > 0 by a Lévy process. Let Kx be the overshoot. We obtain : 1) an asymptotic expansion of the Laplace transform of the distribution of (Tx;Kx), as x tends to infinity ; 2) a polynomial upper bound of the ruin probability ; 3) a convergence in law theorem for the normalized distribution of (Tx;Kx), as x tends to infinity.
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Agnès Volpi. Processus associés à l'équation de diffusion rapide : étude asymptotique du temps de ruine et de l'overshoot. Mathématiques générales [math.GM]. Université Henri Poincaré - Nancy 1, 2003. Français. ⟨NNT : 2003NAN10062⟩. ⟨tel-01748138⟩

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