Contents:Front Cover; 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 Equation2.4 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 Solution4.4 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 Equation6.2 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 Systems9.2 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;
Preliminaries and formulution of the stochastic equations -- Some random integral equations of the Volterra type with applications -- Approximate solution of the random Volterra integral equation and an application to population growth modeling -- Stochastic integral equaltion of the Fredholm type and some applications -- Random discrete Fredholm and Volterra systems -- Nonlinear perturbed random integral eqautions and applications to biological systems -- On a nonlinear random integral equation with application to stochastic chemical kinetics -- Stochastic integral equations of the Ito type -- Stochastic nonlinear differential systems -- Stochastic integrodifferential systems.