UID:
almahu_9947363379202882
Format:
XVI, 400 p.
,
online resource.
ISBN:
9789401137126
Series Statement:
Mathematics and Its Applications ( East European Series ), 40
Note:
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 to Turbulent 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.
In:
Springer eBooks
Additional Edition:
Printed edition: ISBN 9781402003455
Language:
English
DOI:
10.1007/978-94-011-3712-6
URL:
http://dx.doi.org/10.1007/978-94-011-3712-6
