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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. - Examples. - 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.
