《正倒向隨機微分方程最優控》是2019年科學出版社出版的圖書，作者是張良泉。
基本介紹
- 中文名：正倒向隨機微分方程最優控
- 作者：張良泉
- ISBN：9787030612991
- 出版社：科學出版社
- 出版時間：2019-01-01
內容簡介,圖書目錄,
內容簡介
本書內容涉及正倒向隨機微分方程/次優控制系統研究，分兩部分：一，動態規劃原理，我們推導出Hamilton-Jacobi-BellmanInequality，此項研究是深入菲爾茨獎得主，法國數學家P.-L.Lions教授提出的用粘性解理論研究導數有約束的偏微分方程的問題。同時給出在粘性解意義下，隨機遞歸系統的控制驗證定理，通過該定理可以給出反饋控制。第二部分：Pontryagin大值原理.我們先給出控制區域非凸，擴散項不含控制的正倒向完全耦合重隨機系統的大值原理出發，後在第三章回答當控制區域非凸，擴散項含有控制的次優控制原理。另一方面，我們通過動態規劃也給出值函式與次優軌道，以及伴隨方程之間的聯繫。
圖書目錄
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
