Cours de probabilités et calcul stochastique

Ce cours est un cours de niveau master donnant une introduction au calcul stochastique, avec rappel de probabilités et applications aux mathématiques financières

A mesomodel for localisation and damage computation in laminates

International audienceThe basic aspects of a material mesomodel dedicated to composite laminates and capable of simulating complete fracture phenomena are discussed. Attention is focused herein on damage computation and, in particular, on the description of localisation phenomena. Both quasi-static and dynamic loadings are considered

Second-order linear hyperbolic SPDEs driven by isotropic Gaussian noise on a sphere

We study a class of linear hyperbolic stochastic partial differential equations in bounded domains, that includes the wave equation and the telegraph equation, driven by Gaussian noise that is white in time but not in space. We give necessary and sufficient conditions on the spatial correlation of the noise for the existence (and uniqueness) of square-integrable solutions. In the particular case where the domain is a ball and the noise is concentrated on a sphere, we characterize the isotropic Gaussian noises with this property. We also give explicit necessary and sufficient conditions when the domain is a hypercube and the Gaussian noise is concentrated on a hyperplane