1 Stochastic Integral

1.1 Variation

1.2 Random Variable

1.3 Stochastic Processes

1.4 Brownian Motions

1.5 Stochastic Integrals

1.6 It？ Formula

1.7 Important Inequalities

2 Stochastic Differential Equations

2.1 Global Solution

2.2 Almost Surely Asymptotic Estimates

2.3 Stability

2.4 Stabilization

2.5 Convergence of Numerical Methods

3 Stochastic Differential Delay Equations

3.1 Global Solution

3.2 Stability

3.3 Stabilization

3.4 Strong Convergence

3.5 Stability of Numerical Method

3.6 Stochastic Pantograph Equations

4 Stochastic Functional Differential Equations

4.1 Global Solution

4.2 Boundedness and Moment Stability

4.3 SFDE with Infinite Delay

4.4 Stabilization

4.5 Stability of Numerical Method

4.6 Stochastic Differential Equations with Variable Delay

5 Neutral Stochastic Functional Differential Equations

5.1 Global Solution

5.2 Boundedness and Moment Stability

5.3 NSFDEs with Infinite Delay

5.4 Exponential Stability of Numerical Solution

5.5 Neutral Stochastic Differential Delay Equation

6 Stochastic Kolmogorov-Type Systems

6.1 Global Positive Solution

6.2 Moment Boundedness

6.3 Asymptotic Properties

6.4 Stochastic Kolmogorov-type System with Infinite Delay

7 Stochastic Differential Equations with Markovian Switching

7.1 Basic Markov Switching

7.2 Polynomial Growth of Switching SDE

7.3 Polynomial Growth of Switching Neutral Type Equations

References