Random Differential Equations in Science and Engineering

Name: Random Differential Equations in Science and Engineering
Brand: Academic Press
Price: 108.0 EUR
Availability: OnlineOnly

Soong(Autor*in)

Soong(Herausgeber*in)

Academic Press

Erschienen am 14. Mai 2014

343 Seiten

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978-0-08-095612-1 (ISBN)

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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

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