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＜電子ブック＞
Stochastic Differential Equations : With Applications to Physics and Engineering / by K. Sobczyk
(Mathematics and its Applications, East European Series ; 40)

版	1st ed. 1991.
出版者	(Dordrecht : Springer Netherlands : Imprint: Springer)
出版年	1991
本文言語	英語
大きさ	XVI, 400 p : online resource
著者標目	*Sobczyk, K author SpringerLink (Online service)
件　名	LCSH:Probabilities LCSH:Multibody systems LCSH:Vibration LCSH:Mechanics, Applied LCSH:Measure theory FREE:Probability Theory FREE:Multibody Systems and Mechanical Vibrations FREE:Measure and Integration
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-94-011-3712-6

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