Probabilistic Methods in Applied Physics

1. Front Matter

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2. The approximation and the generation of stationary vector processes

   • D. Ammon, W. Wedig

   Pages 1-16

3. Numerical methods and mathematical aspects for simulation of homogeneous and non homogeneous gaussian vector fields

   • F. Poirion, C. Soize

   Pages 17-53

4. Simulation of stochastic differential systems

   • Denis Talay

   Pages 54-96

5. Lyapunov exponents indicate stability and detect stochastic bifurcations

   • Petra Boxler

   Pages 97-119

6. Pitchfork and Hopf bifurcations in stochastic systems — Effective methods to calculate Lyapunov exponents

   • Walter Wedig

   Pages 120-148

7. Stochastic center as a tool in a stochastic bifurcation theory

   • Petra Boxier

   Pages 149-166

8. Lyapunov exponents for a class of hyperbolic random equations

   • Ina Lindemann

   Pages 167-181

9. Functional analysis in stochastic modelling

   • P. Krée

   Pages 182-198

10. Pullback of measures and singular conditioning

    • P. Bernard, P. Krée

    Pages 199-222

11. Adaptive sub-optimal parametric control for non-linear stochastic systems. Application to semi-active isolators

    • S. Bellizzi, R. Bouc

    Pages 223-238

12. Optimal ergodic control of nonlinear stochastic systems

    • Fabien Campillo

    Pages 239-269

13. Stochastic dynamics of hysteretic media

    • Fabio Casciati

    Pages 270-283

14. 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

    • Christian Soize

    Pages 284-309

15. Power spectra of nonlinear dynamic systems — Analysis via generalized Hermite polynomials

    • W. Wedig

    Pages 310-326

16. Some remarks concerning convergence of orthogonal polynomial expansions

    • Pierre Bernard

    Pages 327-334

17. Un Solveur de Wiener Rapide: Résolution des Systèmes de Toeplitz par une Méthode de Gradient Conjugué Préconditionné

    • P. Fayol

    Pages 335-393

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.

• Fokker-Planck equation
• Pitch
• control
• dynamical systems
• modeling
• simulation
• statistics
• fluid- and aerodynamics

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