诺森正倒向随机微分方程控制张良泉9787030612991科学出版社

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
 .  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 dratic 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 Assutin
 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

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
 .  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 dratic 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 Assutin
 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

本书内容涉及正倒向随机微分方程/次优控制
系统研究，分两部分：，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，法数学P.L.Lions教授提
出的用粘解理论研究导数有约束的偏微分方程的问
题。同时给出在粘解意义下，随机递归系统的
控制验定理，通过该定理可以给出反馈控制。
第二部分：Pontryagin值原理.我们先给出控制区
域非凸，扩散项不含控制的正倒向完全耦合重随机系
统的值原理出发，后在第三章回答当控制区域非
凸，扩散项含有控制的次优控制原理。另一方面，我
们通过动态规划也给出值函数与次优轨道，以及伴随
方程之间的联系。