Stochastic Differential Equations

Inhaltsverzeichnis

• Introduction: Origin of Stochastic Differential Equations.
• I. Stochastic Processes — Short ResumÉ.
• 1. Introductory Remarks.
• 2. Probability and Random Variables.
• 3. Stochastic Processes — Basic Concepts.
• 4. Gaussian Processes.
• 5. Stationary Processes.
• 6. Markov Processes.
• 7. Processes With Independent Increments; Wiener Process And Poisson Process.
• 8. Point Stochastic Processes.
• 9. Martingales.
• 10. Generalized Stochastic Processes; White Noise.
• 11. Processes with Values in Hilbert Space.
• 12. Stochastic Operators.
• Examples.
• II. Stochastic Calculus: Principles and Results.
• 13. Introductory Remarks.
• 14. Processes of Second Order; Mean Square Analysis.
• 15. Analytical Properties of Sample Functions.
• 16. ITÔ Stochastic Integral.
• 17. Stochastic Differentials. ITÔ Formula.
• 18. Counting Stochastic Integral.
• 19. Generalizations.
• III. Stochastic Differential Equations: Basic Theory.
• 20. Introductory Remarks.
• 21. Regular Stochastic Differential Equations.
• 22. ITÔ Stochastic Differential Equations.
• 23. Stochastic Abstract Differential Equations.
• IV. Stochastic Differential Equations: Analytical Methods.
• 24. Introductory Remarks.
• 25. Systems with Random Initial Conditions.
• 26. Linear Systems with Random Excitation.
• 27. Nonlinear Systems with Random Excitation.
• 28. Stochastic Systems.
• 29. Stochastic Partial Differential Equations.
• V. Stochastic Differential Equations: Numerical Methods.
• 30. Introductory Remarks.
• 31. Deterministic Equations: Basic Numerical Methods.
• 32. Approximate Schemes for Regular Stochastic Equations.
• 33. Numerical Integration of ITÔ Stochastic Equations.
• VI. Applications: Stochastic Dynamics of Engineering Systems.
• 34. Introduction.
• 35. Random Vibrations of Road Vehicles.
• 36. Response of Structures toTurbulent Field.
• 37. Response of Structures To Earthquake Excitation.
• 38. Response of Structures to Sea Waves.
• 39. Stochastic Stability of Structures.
• 40. Other Problems.
• Appendix..
• A.1. Cauchy formula.
• A.2. Gronwall-Bellman inequality.
• References.