非线性随机微分方程

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)

本书主要介绍了It型非线性随机微分方程，包括时滞随机微分方程和中立型随机微分方程的基本理论，深入讨论了非线性随机微分方程的稳定性、稳定化及其数值方法的收敛性及稳定性等。此外，本书还综述了近年来国内外非线性随机微分方程最新研究成果。

适读人群 ：高等院校数学系本科生、研究生、高校教师、研究工作涉及随机微分方程的科技工作者

该书是全英文版专业教材，介绍了最新研究成果，内容严谨，具备一定的先进性。