Random Differential Equations in Science and Engineering
Published on 14. May 2014
343 pages
978-0-08-095612-1 (ISBN)
Description
Random Differential Equations in Science and Engineering
More details
Series
Language
English
Place of publication
Oxford
United States
ISBN-13
978-0-08-095612-1 (9780080956121)
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Schweitzer Classification
Other editions
Additional editions
Book
07/1973
Academic Press
€84.32
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Content
- Front Cover
- Random Differential Equations in Science and Engineering
- Copyright Page
- Contents
- Preface
- Acknowledgments
- Chapter 1. Introduction
- Chapter 2. Probability and Random Variables: A Review
- 2.1. Elements of Set Theory
- 2.2. Axioms of Probability and Probability Spaces
- 2.3. Random Variables
- 2.4. Functions and Random Variables
- 2.5. The Gaussian Random Variable and the Central Limit Theorem
- References
- Problems
- Chapter 3. Stochastic Processes and Their Classifications
- 3.1. Basic Concepts of Stochastic Processes
- 3.2. Classification Based upon Regularity
- 3.3. Classification Based upon Memory
- 3.4. The Gaussian Stochastic Process
- References
- Problems
- Chapter 4. Stochastic Limits and Calculus in Mean Square
- 4.1. Preliminary Remarks
- 4.2. Convergence of a Sequence of Random Variables
- 4.3. Mean Square Continuity
- 4.4. Mean Square Differentiation
- 4.5. Mean Square Integration
- 4.6. Distributions of Mean Square Derivatives and Integrals
- References
- Problems
- Chapter 5. Random Ordinary Differential Equations
- 5.1. Existence and Uniqueness
- 5.2. The Ito Equation
- 5.3. General Remarks on the Solution Process
- 5.4. Classification of Random Differential Equations
- References
- Problems
- Chapter 6. Differential Equations with Random Initial Conditions
- 6.1. The Mean Square Theory
- 6.2. Statistical Properties of the Solution Process
- References
- Problems
- Chapter 7. Differential Equations with Random Inhomogeneous Parts
- 7.1. The Mean Square Theory
- 7.2. Solution Processes for Linear Equations
- 7.3. The Case of Markov Processes
- 7.4. Solution Processes for Nonlinear Equations
- Problems
- References
- Chapter 8. Differential Equations with Random Coefficients
- 8.1. The Mean Square Theory
- 8.2. First-Order Linear Equations
- 8.3. Differential Equations with Random Constant Coefficients
- 8.4. Differential Equations of the Ito Type
- 8.5. Perturbation Techniques
- 8.6. Truncated Hierarchy Techniques
- References
- Problems
- Chapter 9. Stochastic Stability
- 9.1. Moment Stabilities
- 9.2. Lyapunov Stability
- References
- Problems
- Appendix A. Sample Treatment of Random Differential Equations
- A.1. Stochastic Processes with Continuous Trajectories
- A.2. A Sample Calculus
- A.3. Stochastic Sample Solutions
- References
- Appendix B. Some Useful Properties of the Solution Process
- B.1. Zero and Threshold Crossings
- B.2. Distribution of Extrema
- B.3. Distribution of Intervals between Zeros
- B.4. The First Passage Time Probability
- References
- Author Index
- Subject Index
