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.
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.
