Random integral equations, Volume 96 (Mathematics in Science and Engineering)

✍ Scribed by Bharucha-Reid (editor)

• Publisher: Academic Press
• Year: 1972
• Tongue: English
• Leaves: 283
• Edition: 1
• Category: Library

✦ Table of Contents

Front Cover
Random Integral Equations
Copyright Page
Contents
Preface
Acknowledgments
Introduction
References
Chapter 1. Probability Theory in Banach Spaces: An Introductory Survey
1.1 Introduction
1.2 Banach Spaces
1.3 Banach Space-Valued Random Variables
1.4 Banach Space-Valued Random Functions
1.5 Probability Measures on Banach Spaces
1.6 Limit Theorems
References
Chapter 2. Operator-Valued Random Variables
2.1 Introduction
2.2 Operators on Banach Spaces
2.3 Random Operators
2.4 Spectral Theory of Random Operators
2.5 Operator-Valued Random Functions
2.6 Limit Theorems
References
Chapter 3. Random Equations: Basic Concepts and Methods of Solution
3.1 Introduction
3.2 Random Equations: Basic Concepts and Examples
3.3 The Solution of Random Equations
3.4 Some Measure-Theoretic and Statistical Problems Associated with Random Equations
References
Chapter 4. Random Linear Integral Equations
4.1 Introduction
4.2 Fredholm and Volterra Integral Equations with Random Forcing Functions
4.3 Fredholm and Volterra Integral Equations with Random Kernels
4.4 Some Random Linear Integral Equations Which Arise in Applied Problems
References
Chapter 5. Eigenvalue Problems for Random Fredholm Equations
5.1 Introduction
5.2 Fredholm Integral Equations with Random Degenerate Kernels
5.3 Fredholm Integral Equations with Random Symmetric Kernels
References
Chapter 6. Random Nonlinear Integral Equations
6.1 Introduction
6.2 Integral Equation Formulation of Some Random Nonlinear Differential Equations
6.3 A Nonlinear Integral Equation with Random Right-Hand Side
6.4 Nonlinear Integral Equations of Volterra Type with Random Kernels and Random Right-Hand Sides
6.5 Random Nonlinear Integral Equations of Uryson Type
6.6 A Measure-Theoretic Problem Associated with a Non- linear Integrodifferential Equation with Random Right-Hand Side
6.7 Some Random Nonlinear Integral Equations Which Arise in Applied Problems
References
Chapter 7. Itô Random Integral Equations
7.1 Introduction
7.2 Itô Random Integral Equations: Basic Theory
7.3 Itô Random Integral Equations in Hilbert Spaces
7.4 Some Additional Studies on Itô Equations and Their Applications
References
Author Index
Subject Index