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

Theory of molecular excitation and relaxation near a plasmonic device

International audienceThe new optical concepts currently developed in the research field of plasmonics can have significant practical applications for integrated optical device miniaturization as well as for molecular sensing applications. Particularly, these new devices can offer interesting opportunities for optical addressing of quantum systems. In this article, we develop a realistic model able to explore the various functionalities of a plasmon device connected to a single fluorescing molecule. We show that this theoretical method provides a useful framework to understand how quantum and plasmonic entities interact in a small area. Thus, the fluorescence signal evolution from excitation control to relaxation control depending on the incident light power is clearly observed