Probabilistic Methods in Applied Physics

D. Ammon, W. Wedig (auth.), Paul Krée, Walter Wedig (eds.)3540602143, 9783540602149

This book is an outcome of a European collaboration on applications of stochastical methods to problems of science and engineering. The articles present methods allowing concrete calculations without neglecting the mathematical foundations. They address physicists and engineers interested in scientific computation and simulation techniques. In particular the volume covers: simulation, stability theory, Lyapounov exponents, stochastic modelling, statistics on trajectories, parametric stochastic control, Fokker Planck equations, and Wiener filtering.

---

Table of contents :
The approximation and the generation of stationary vector processes….Pages 1-16
Numerical methods and mathematical aspects for simulation of homogeneous and non homogeneous gaussian vector fields….Pages 17-53
Simulation of stochastic differential systems….Pages 54-96
Lyapunov exponents indicate stability and detect stochastic bifurcations….Pages 97-119
Pitchfork and Hopf bifurcations in stochastic systems — Effective methods to calculate Lyapunov exponents….Pages 120-148
Stochastic center as a tool in a stochastic bifurcation theory….Pages 149-166
Lyapunov exponents for a class of hyperbolic random equations….Pages 167-181
Functional analysis in stochastic modelling….Pages 182-198
Pullback of measures and singular conditioning….Pages 199-222
Adaptive sub-optimal parametric control for non-linear stochastic systems. Application to semi-active isolators….Pages 223-238
Optimal ergodic control of nonlinear stochastic systems….Pages 239-269
Stochastic dynamics of hysteretic media….Pages 270-283
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….Pages 284-309
Power spectra of nonlinear dynamic systems — Analysis via generalized Hermite polynomials….Pages 310-326
Some remarks concerning convergence of orthogonal polynomial expansions….Pages 327-334
Un Solveur de Wiener Rapide: Résolution des Systèmes de Toeplitz par une Méthode de Gradient Conjugué Préconditionné….Pages 335-393