非线性随机微分方程 英文PDF电子书下载

1 Stochastic Integral 1

1.1 Variation 2

1.2 Random Variable 3

1.3 Stochastic Processes 9

1.4 Brownian Motions 15

1.5 Stochastic Integrals 21

1.6 It？ Formula 28

1.7 Important Inequalities 32

2 Stochastic Differential Equations 35

2.1 Global Solution 35

2.2 Almost Surely Asymptotic Estimates 52

2.3 Stability 54

2.4 Stabilization 63

2.5 Convergence of Numerical Methods 73

3 Stochastic Differential Delay Equations 84

3.1 Global Solution 84

3.2 Stability 94

3.3 Stabilization 103

3.4 Strong Convergence 114

3.5 Stability of Numerical Method 124

3.6 Stochastic Pantograph Equations 134

4 Stochastic Functional Differential Equations 144

4.1 Global Solution 144

4.2 Boundedness and Moment Stability 154

4.3 SFDE with Infinite Delay 165

4.4 Stabilization 181

4.5 Stability of Numerical Method 189

4.6 Stochastic Differential Equations with Variable Delay 200

5 Neutral Stochastic Functional Differential Equations 215

5.1 Global Solution 215

5.2 Boundedness and Moment Stability 224

5.3 NSFDEs with Infinite Delay 236

5.4 Exponential Stability of Numerical Solution 246

5.5 Neutral Stochastic Differential Delay Equation 256

6 Stochastic Kolmogorov-Type Systems 265

6.1 Global Positive Solution 266

6.2 Moment Boundedness 271

6.3 Asymptotic Properties 274

6.4 Stochastic Kolmogorov-type System with Infinite Delay 278

7 Stochastic Differential Equations with Markovian Switching 286

7.1 Basic Markov Switching 287

7.2 Polynomial Growth of Switching SDE 289

7.3 Polynomial Growth of Switching Neutral Type Equations 300

References 306