正倒向随机微分方程最优控制 英文版
作者：张良泉 著
出版时间： 2019年版
内容简介
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：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下，随机递归系统的控制验证定理，通过该定理可以给出反馈控制。第二部分：Pontryagin大值原理.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大值原理出发，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。
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目录
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
