Probabilistic Methods in Applied Physics

The approximation and the generation of stationary vector processes.- Numerical methods and mathematical aspects for simulation of homogeneous and non homogeneous gaussian vector fields.- Simulation of stochastic differential systems.- Lyapunov exponents indicate stability and detect stochastic bifurcations.- Pitchfork and Hopf bifurcations in stochastic systems - Effective methods to calculate Lyapunov exponents.- Stochastic center as a tool in a stochastic bifurcation theory.- Lyapunov exponents for a class of hyperbolic random equations.- Functional analysis in stochastic modelling.- Pullback of measures and singular conditioning.- Adaptive sub-optimal parametric control for non-linear stochastic systems. Application to semi-active isolators.- Optimal ergodic control of nonlinear stochastic systems.- Stochastic dynamics of hysteretic media.- Exact steady-state solution of FKP equation in higher dimension for a class of non linear Hamiltonian dissipative dynamical systems excited by Gaussian white noise.- Power spectra of nonlinear dynamic systems - Analysis via generalized Hermite polynomials.- Some remarks concerning convergence of orthogonal polynomial expansions.- Un Solveur de Wiener Rapide: Résolution des Systèmes de Toeplitz par une Méthode de Gradient Conjugué Préconditionné.