Random Integral Equations with Applications to Life Sciences and Engineering (Mathematics in Science and Engineering)

✍ Scribed by Chris P. Tsokos, W.J. Padgett

• Publisher: Academic Press
• Year: 1974
• Tongue: English
• Leaves: 289
• Edition: 1
• Category: Library

✦ Synopsis

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;
methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and
methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.

As a result, the book represents a blend of new methods in general computational analysis,
and specific, but also generic, techniques for study of systems theory ant its particular
branches, such as optimal filtering and information compression.

- Best operator approximation,
- Non-Lagrange interpolation,
- Generic Karhunen-Loeve transform
- Generalised low-rank matrix approximation
- Optimal data compression
- Optimal nonlinear filtering

✦ Table of Contents

Random Integral Equations With Applications to Life Sciences and Engineering
Copyright Page
Contents
Preface
General Introduction
Chapter I. Preliminaries and Formulation of the Stochastic Equations
1.0 Introduction
1.1 Basic Definitions and Theorems from Functional Analysis
1.2 Probabilistic Definitions
1.3 The Stochastic Integral Equations and Stochastic Differential Systems
Appendix 1.A
Chapter II. Some Random Integral Equations of the Volterra Type with Applications
2.0 Introduction
2.1 The Random Integral Equation
2.2 Some Applications of the Equation
2.3 The Random Integral Equation
2.4 Applications of the Integral Equation
Chapter III. Approximate Solution of the Random Volterra Integral Equation and an Application to Population Growth Modeling
3.0 Introduction
3.1 The Method of Successive Approximations
3.2 A New Stochastic Formulation of a Population Growth Problem
3.3 Method of Stochastic Approximation
Chapter IV. A Stochastic Integral Equation of the Fredholm Type and Some Applications
4.0 Introduction
4.1 Existence and Uniqueness of a Random Solution
4.2 Some Special Cases
4.3 Stochastic Asymptotic Stability of the Random Solution
4.4 An Application in Stochastic Control Systems
4.5 A Random Perturbed Fredholm Integral Equation
Chapter V. Random Discrete Fredholm and Volterra Systems
5.0 Introduction
5.1 Existence and Uniqueness of a Random Solution of System (5.0.1)
5.2 Special Cases of Theorem 5.1.2
5.3 Stochastic Stability of the Random Solution
5.4 An Approximation to System (5.0.1 )
5.5 Application to Stochastic Control Systems
Chapter VI. Nonlinear Perturbed Random Integral Equations and Application to Biological Systems
6.0 Introduction
6.1 The Random Integral Equation
6.2 Applications to Biological Systems
Chapter VII. On a Nonlinear Random Integral Equation with Application to Stochastic Chemical Kinetics
7.0 Introduction
7.1 Mathematical Preliminaries
7.2 An Existence and Uniqueness Theorem
7.3 A Stochastic Chemical Kinetics Model
Chapter VIII. Stochastic Integral Equations of the Ito Type
8.0 Introduction
8.1 Preliminary Remarks
8.2 On an Ito Stochastic Integral Equation
8.3 On Ito–Doob–Type Stochastic Integral Equations
Chapter IX. Stochastic Nonlinear Differential Systems
9.0 Introduction
9.1 Reduction of the Stochastic Differential Systems
9.2 Stochastic Absolute Stability of the Differential Systems
Appendix 9.A
Chapter X. Stochastic Integrodifferential Systems
10.0 Introduction
10.1 The Stochastic Integrodifferential Equation
10.2 Reduction of the Stochastic Nonlinear Integrodifferential Systems with Time Lag
10.3 Stochastic Absolute Stability of the Systems
Bibliography
Index