Preface
Chapter 1 Preliminaries
1.1 Probability and Random Variables
1.1.1 Probability Spaces
1.1.2 Convergence of Probabilities
1.2 Stochastic Processes
1.2.1 Continuous Time Martingales
1.2.2 Stochastic Integration
1.3 The Basic Theory of FBSDEs
1.3.1 A Black-Scholes Formula in Finance
1.3.2 Formulations of Stochastic Optimal Control Problems
Bibliography
Chapter 2 Singular Optimal Controls of Stochastic Recursive Systems and H-J-B Inequality
2.1 Introduction
2.2 Formulation of the Problem
2.3 Dynamic Programming Principle
2.4 Example
2.5 Appendix
Bibliography
Chapter 3 Stochastic Verification Theorem of Forward-Backward Controlled Systems for Viscosity Solutions
3.1 Introduction
3.2 Super-differentials, Sub-differentials, and Viscosity Solutions
3.3 Stochastic Verification Theorem for Forward-Backward Controlled Systems...
3.4 Optimal Feedback Controls
Bibliography
Chapter 4 Maximum Principle for Forward-Backward Doubly Stochastic Control Systems and Applications
4.1 Introduction
4.2 Statement of the Problem
4.3 Variational Equations and Variational Inequalities
4.4 The Maximum Principle in Global Form
4.5 Applications to Optimal Control Problems of Stochastic PDEs
4.6 Linear Quadratic Nonzero Sum Doubly Stochastic Differential Games
Bibliography
Chapter 5 Stochastic Maximum Principle for Near-Optimal Control of FBSDEs
5.1 Introduction
5.2 Formulation of the Optimal Control Problem and Basic Assumptions
5.3 Main Results
5.3.1 Necessary Condition of Near-Optimality
5.3.2 Sufficient Condition of Near-Optimality
5.4 Examples
5.5 Concluding Remarks
5.6 Appendix
Bibliography
Chapter 6 Near Optimal Control of Stochastic Recursive Systems via Viscosity Solution
6.1 Introduction
6.2 Preliminaries and Notations
6.3 Main Results
6.4 Conclusions
Bibliography
Chapter 7 Asymptotic Properties of Coupled Forward-Backward Stochastic Differential Equations
7.1 Introduction
7.2 Preliminaries
7.3 Regularity of the solution of FBSDEs
7.4 Main Results
7.4.1 Convergence of distributions
7.4.2 Large deviation principle
Bibliography

本书内容涉及正倒向随机微分方程最优/次优控制系统研究，分两部分：第一，动态规划原理，我们推导出Hamilton-Jacobi-BellmanInequality，此项研究是深入菲尔茨奖得主，法国数学家P。-L。Lions教授提出的用粘性解理论研究导数有约束的偏微分方程的问题。同时给出在粘性解意义