| Preface to the Second Edition |
| Preface to the First Edition |
| Introduction / 1： |
| Modeling by Stochastic Differential Equations / 1.1： |
| Framework / 2： |
| White Noise / 2.1： |
| The 1-Dimensional, d-Parameter Smoothed White Noise / 2.1.1： |
| The (Smoothed) White Noise Vector / 2.1.2： |
| The Wiener-Itô Chaos Expansion / 2.2： |
| Chaos Expansion in Terms of Hermite Polynomials / 2.2.1： |
| Chaos Expansion in Terms of Multiple Itô Integrals / 2.2.2： |
| The Hida Stochastic Test Functions and Stochastic Distributions. The Kondratiev Spaces (S)m;N, (S)m;N-? / 2.3： |
| The Hida Test Function Space (S) and the Hida Distribution Space (S)* / 2.3.1： |
| Singular White Noise / 2.3.2： |
| The Wick Product / 2.4： |
| Some Examples and Counterexamples / 2.4.1： |
| Wick Multiplication and Hitsuda/Skorohod Integration / 2.5： |
| The Hermite Transform / 2.6： |
| The (S)N?,r Spaces and the S-Transform / 2.7： |
| The Topology of (S)N-1 / 2.8： |
| The F-Transform and the Wick Product on L1(&mu) / 2.9： |
| The Wick Product and Translation / 2.10： |
| Positivity / 2.11： |
| Applications to Stochastic Ordinary Differential Equations / 3： |
| Linear Equations / 3.1： |
| Linear 1-Dimensional Equations / 3.1.1： |
| Some Remarks on Numerical Simulations / 3.1.2： |
| Some Linear Multidimensional Equations / 3.1.3： |
| A Model for Population Growth in a Crowded, Stochastic Environment / 3.2： |
| The General (S)-1 Solution / 3.2.1： |
| A Solution in L1(&mu) / 3.2.2： |
| A Comparison of Model A and Model B / 3.2.3： |
| A General Existence and Uniqueness Theorem / 3.3： |
| The Stochastic Volterra Equation / 3.4： |
| Wick Products Versus Ordinary Products: a Comparison Experiment / 3.5： |
| Variance Properties / 3.5.1： |
| Solution and Wick Approximation of Quasilinear SDE / 3.6： |
| Using White Noise Analysis to Solve General Nonlinear SDEs / 3.7： |
| Stochastic Partial Differential Equations Driven by Brownian White Noise / 4： |
| General Remarks / 4.1： |
| The Stochastic Poisson Equation / 4.2： |
| The Functional Process Approach / 4.2.1： |
| The Stochastic Transport Equation / 4.3： |
| Pollution in a Turbulent Medium / 4.3.1： |
| The Heat Equation with a Stochastic Potential / 4.3.2： |
| The Stochastic Schrödinger Equation / 4.4： |
| L1(&mu)Properties of the Solution / 4.4.1： |
| The Viscous Burgers Equation with a Stochastic Source / 4.5： |
| The Stochastic Pressure Equation / 4.6： |
| The Smoothed Positive Noise Case / 4.6.1： |
| An Inductive Approximation Procedure / 4.6.2： |
| The 1-Dimensional Case / 4.6.3： |
| The Singular Positive Noise Case / 4.6.4： |
| The Heat Equation in a Stochastic, Anisotropic Medium / 4.7： |
| A Class of Quasilinear Parabolic SPDEs / 4.8： |
| SPDEs Driven by Poissonian Noise / 4.9： |
| Stochastic Partial Differential Equations Driven by Lévy Processes / 5： |
| The White Noise Probability Space of a Lévy Process (d = 1) / 5.1： |
| White Noise Theory for a Lévy Process (d = 1) / 5.3： |
| Chaos Expansion Theorems / 5.3.1： |
| The Lévy-Hida-Kondratiev Spaces / 5.3.2： |
| White Noise Theory for a Lévy Field (d ≥ l) / 5.4： |
| Construction of the Lévy Field / 5.4.1： |
| Chaos Expansions and Skorohod Integrals (d ≥ 1) / 5.4.2： |
| Waves in a Region with a Lévy White Noise Force / 5.4.3： |
| Heat Propagation in a Domain with a Lévy White Noise Potential / 5.7： |
| Appendix A |
| Appendix B |
| Appendix C |
| Appendix D |
| Appendix E |
| References |
| List of frequently used notation and symbols |
| Index |
| Preface to the Second Edition |
| Preface to the First Edition |
| Introduction / 1： |
