Stochastic Differential Equations: With Applications to Physics and Engineering / Edition 1

by K. Sobczyk

Overview

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Product Details

ISBN-13:	9780792303398
Publisher:	Springer Netherlands
Publication date:	02/28/1991
Series:	Mathematics and its Applications , #40
Edition description:	1991
Pages:	400
Product dimensions:	6.10(w) x 9.25(h) x 0.24(d)

Table of Contents

Introduction: Origin of Shastic Differential Equations.- I. Shastic Processes — Short ResumÉ.- 1. Introductory Remarks.- 2. Probability and Random Variables.- 3. Shastic Processes — Basic Concepts.- 4. Gaussian Processes.- 5. Stationary Processes.- 6. Markov Processes.- 7. Processes With Independent Increments; Wiener Process And Poisson Process.- 8. Point Shastic Processes.- 9. Martingales.- 10. Generalized Shastic Processes; White Noise.- 11. Processes with Values in Hilbert Space.- 12. Shastic Operators.- Examples.- II. Shastic Calculus: Principles and Results.- 13. Introductory Remarks.- 14. Processes of Second Order; Mean Square Analysis.- 15. Analytical Properties of Sample Functions.- 16. ITÔ Shastic Integral.- 17. Shastic Differentials. ITÔ Formula.- 18. Counting Shastic Integral.- 19. Generalizations.- Examples.- III. Shastic Differential Equations: Basic Theory.- 20. Introductory Remarks.- 21. Regular Shastic Differential Equations.- 22. ITÔ Shastic Differential Equations.- 23. Shastic Abstract Differential Equations.- IV. Shastic 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. Shastic Systems.- 29. Shastic Partial Differential Equations.- V. Shastic Differential Equations: Numerical Methods.- 30. Introductory Remarks.- 31. Deterministic Equations: Basic Numerical Methods.- 32. Approximate Schemes for Regular Shastic Equations.- 33. Numerical Integration of ITÔ Shastic Equations.- VI. Applications: Shastic 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. Shastic Stability of Structures.- 40. Other Problems.- Appendix..- A.1. Cauchy formula.- A.2. Gronwall-Bellman inequality.- References.

Editorial Reviews

Sobczyk provides a unified treatment of both regular (or, random) and Ito stochastic differential equations, focusing on solution methods, including some recently developed. Special concern is given to both the mathematical structure and the most efficient solution methods (analytical as well as numerical). Starting from basic notions and results of stochastic processes and calculus, many principal mathematical problems and results related to stochastic differential equations are expounded. Applications treated include those relating to road vehicles, earthquake excitations, and offshore structures. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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