Dynamique de structures soumises `a des sollicitations al´eatoires : analyse math´ematique et r´esolution num´erique des ´equations diff´erentielles stochastiques

Abstract

This thesis treats numerical technics for solving stochastic differential equations, we have derived a family of semi-implicit schemes of weak order N = 3.0 (general case) and N = 4.0 (additive noise case). A numerical experiments confirming the theoricals results are schown. We present a complete study of mean-square stability of a family depending on two parameter of weak order 2.0 for solving SDE, this is a extension of the work of D.J.Higham for the theta-methods.