Stochastic Differential Equations

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.