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《Stochastic versus Deterministic Systems of Differential Equation》
文件格式：pdf
作者：G. S. LADDE M. SAMBANDHAM
出版日期：2004年
共339页
CONTENTS
Preface iii
Notation and Abbreviations xi
Chapter 1: Random Polynomials
1.0 Introduction 1
1.1 Upper Bound for Mean Deviation 1
1.2 Error Estimates 4
1.3 Eigenvalues of Random Matrices 10
1.4 Stability of Random Matrices 21
1.5 Applications 24
a) Economic Analysis of Capital and Investment 25
b) Free Damped Motion of Spring 26
1.6 Numerical Examples 27
1.7 Notes and Comments 35
Chapter 2: Ordinary Differential Systems with
Random Parameters
2.0 Introduction 37
2.1 Variation of Constants Method 38
2.2 Comparison Method 45
2.3 Probability Distribution Method 58
2.4 Stability Analysis 66
2.5 Error Estimates 83
2.6 Relative Stability 100
2.7 Applications to Population Dynamics 110
2.8 Numerical Examples 122
2.9 Notes and Comments 129
Vll
viii Contents
Chapter 3: Boundary Value Problems with
Random Parameters
3.0 Introduction 131
3.1 Green's Function Method 132
3.2 Comparison Method 139
3.3 Probability Distribution Method 150
3.4 Solvability and Uniqueness Analysis 165
3.5 Stability Analysis 169
3.6 Error Estimates 174
3.7 Relative Stability 180
3.8 Applications to Physical Systems 184
a) Slider and Rigid Roller Bearing Problems 184
b) The Hanging Cable Problem 208
3.9 Numerical Examples 213
3.10 Notes and Comments 217
Chapter 4: Ito-Type Stochastic Differential Systems
4.0 Introduction 219
4.1 Variation of Constants Method 220
4.2 Comparison Method 227
4.3 Probability Distribution Method 234
4.4 Stability Analysis 238
4.5 Error Estimates 245
4.6 Relative Stability 252
4.7 Applications to Population Dynamics 255
4.8 Numerical Examples 262
4.9 Notes and Comments 266
Contents ix
Chapter 5: Boundary Value Problems of Ito-Type
5.0 Introduction 267
5.1 Green's Function Method 267
5.2 Stability Analysis 277
5.3 Error Estimates 280
5.4 Relative Stability 285
5.5 Notes and Comments 287
APPENDIX
A.O Introduction 289
A.I Convergence of Random Sequences 289
A.2 Initial Value Problems 291
A.3 Boundary Value Problems 298
References 301
Index 313
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