Stochastic systems /
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York :
Academic Press,
1983.
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| Series: | Mathematics in science and engineering ;
v. 169. |
| Subjects: | |
| Online Access: | CONNECT CONNECT |
Table of Contents:
- Front Cover; Stochastic Systems; Copyright Page; Contents; Foreword; Preface; Chapter 1. Green's Functions and Systems Theory; 1.1. Introduction: Some Remarks on the Mathematical Modeling of Dynamical Systems; 1.2. Linearity and Superposition; 1.3. The Concept of a Green's Function; 1.4. Simple Input-Output Systems and Green's Functions; 1.5. Operator Forms; 1.6. Green's Function for the Inhomogeneous Sturm-Liouville Operator; 1.7. Properties of the Green's Function; 1.8. Evaluation of the Wronskian; 1.9. Solution Using Abel's Formula
- 1.10. Use of Green's Function to Solve the Inhomogeneous Equation1.11. Adjoint Operators; 1.12. Green's Functions for Adjoint Operators; 1.13. Symbolic Functions; 1.14. Sturm-Liouville Differential Equation; 1.15. Boundary Conditions Specified on a Finite Interval [a, b]; 1.16. Series Expansions for G(x,?); 1.17. Multiple-Input-Multiple-Output Systems; 1.18. Bilinear Form of the Green's Function; 1.19. Bilinear Form of the Green's Function for the Sturm-Liouville Differential Equation; 1.20. Cases Where the Green's Function Does Not Exist; 1.21. Multidimensional Green's Functions
- 1.22. Green's Functions for Initial Conditions1.23. Approximate Calculation of Green's Functions; References; Chapter 2. A Basic Review of the Theory of Stochastic Processes; 2.1. The Nature of a Stochastic Process; 2.2. Stochastic Processes-Basic Definitions; 2.3. Characterization and Classification of Stochastic Processes; 2.4. Consistency Conditions on the Distribution; 2.5. Some Simple Stochastic Processes; 2.6. Time Dependences of Distributions; 2.7. Statistical Measures of Stochastic Processes; 2.8. Random Fields; 2.9. The Calculus of Stochastic Processes
- 2.10. Expansions of Random Functions2.11. Ergodic Theorems; 2.12. Generalized Random Processes; References; Chapter 3. Stochastic Operators and Stochastic Systems; 3.1. Stochastic Systems-Basic Concepts; 3.2. Stochastic Green's Functions; 3.3. Statistical Operators; 3.4. Stochastic Green's Theorem; 3.5. Determination of the Kernel from the Physical Process; References; Chapter 4. Linear Stochastic Differential Equations; 4.1. Stochastic Differential Operators; 4.2. The Differential Equation Formulation; 4.3. Derivation of Stochastic Green's Theorem; 4.4. Hierarchy or Averaging Method
- 4.5. Perturbation Theory4.6. Connection between Perturbation Theory and the Hierarchy Method; 4.7. The Decomposition Method; 4.8. Differential Operator with One Random Coefficient; 4.9. A Convenient Resolvent Kernel Formulation; 4.10. Inverse Operator Form of the Decomposition Method Solution; 4.11. Some Further Remarks on the Operator Identity (4.10.1); 4.12. General Form of the Stochastic Green's Function; 4.13. Random Initial Conditions; 4.14. Simplifying Green's Function Calculations for Higher Order Equations; References; Chapter 5. Nonlinear Stochastic Differential Equations
