随机控制
随机控制封面图

随机控制

雍炯敏, 著

出版社:世界图书出版公司北京公司

年代:2012

定价:68.0

书籍简介:

本书是一部非常系统、完整的研究生教程,也是一部学习控制理论的很好的补充材料。书中有一些原创性的论题是别的图书没能包括的,是学习扩散过程中Pontryagin最大原理和Bellman 动态规划原理之间关系的不二选择。本书权威性强,其中的材料可以运用在数学、工程和金融的随机控制和动态优化课程中。目次:基本随机微积分;随机优化控制问题;最大原理和随机哈密顿体系;动态规划和HJB方程;最大原理和动态规划之间的关系;线性二次优化控制问题;向后随机微分方程。

书籍目录:

Preface

Notation

Assumption Index

Problem Index

Chapter 1. Basic Stochastic Calculus

1. Probability

1.1. Probability spaces

1.2. Random variables

1.3. Conditional expectation

1.4. Convcrgence of probabilities

2. Stochastic Processes

2.1. General considerations

2.2. Brownian motions

3. Stopping Times

4. Martingales

5. ItS's Integral

5.1. Nondifferentiability of Brownian motion

5.2. Definition of Ites integral and basic properties

5.3. ItS's formula

5.4. Martingale representation theorems

6. Stochastic Differential Equations

6.1. Strong solutions

6.2. Weak solutions

6.3. Linear SDEs

6.4. Other types of SDEs

Chapter 2. Stochastic Optimal Control Problems

1. Introduction

2. Deterministic Cases Revisited

3. Examples of Stochastic Control Problems

3. 1. Production planning

3.2. Investment vs. consumption

3.3. Reinsurance and dividend management

3.4. Technology diffusion

3.5. Queueing systems in heavy traffic

4. Formulations of Stochastic Optimal Control Problems

4.1. Strong formulation

4.2. Weak formulation

5. Existence of Optimal Controls

5.1. A deterministic result

5.2. Existence under strong formulation

5.3. Existence under weak formulation

6. Reachable Sets of Stochastic Control Systems

6.1. Nonconvexity of the reachable sets

6.2. Nonclnseness of the reachable sets

7. Other Stochastic Control Models

7.1. Random duration

7.2. Optimal stopping

7.3. Singular and impulse controls

7.4. Risk-sensitive controls

7.5. Ergodic controls

7.6. Partially observable systems

8. Historical Remarks

Chapter 3. Maximum Principle and Stochastic

Hamiitonian Systems

1. Introduction

2. The Deterministic Case Rcvisited

3. Statement of the Stochastic Maximum Principle

3.1. Adjoint equations

3.2. The maximum principle and stochastic

Hamiltonian systems

3.3. A worked-out example

4. A Proof of the Maximum Principle

4.1. A moment estimate

4.2. Taylor expansions

4.3. Duality analysis and complction of thc proof

5. Sufficient Conditions of Optimality

6. Problems with Statc Constraints

6.1. Formulation of the problem and the maximum principle

6.2. Some preliminary lemmas

6.3. A proof of Theorem 6.1

7. Historical Remarks

Chapter 4. Dynamic Programming and HJB Equations

1. Introduction

2. The Deterministic Casc Revisited

3. The Stochastic Principle of Optimality and the HJB Equation

3.1. A stochastic framework for dynamic programming

3.2. Principlc of optimality

3.3. The HJB cquation

4. Other Properties of the Value Function

4.1. Continuous dependence on parameters

4.2. Semiconcavity

5. Viseo~ity Solutions

5.1. Definitions

5.2. Some properties

6. Uniqueness of Viscosity Solutions

6.1. A uniqueness theorem

6.2. Proofs of Lemmas 6.6 and 6.7

7. Historical Rcmarks

Chapter 5. The Relationship Between the Maximum

Principle and Dynamic Programming

1. Introduction

2. Classical Hamilton-Jacobi Theory

3. Relationship for Deterministic Systems

3.1. Adjoint variable and value function: Smooth case

3.2. Economic interpretation

3.3. Methods of characteristics and the Fcynman Kac formula

3.4. Adjoint variable and value function: Nonsmooth case

3.5. Vcrification theorems

4. Relationship for Stochastic Systems

4.1. Smooth case

4.2. Nonsmooth case: Differentials in the spatial variable

4.3. Nonsmooth case: Differentials in the time variable

5. Stochastic Vcrification Theorems

5.1. Smooth case

5.2. Nonsmooth case

6. Optimal Fccdback Controls

7. Historical Remarks

Chapter 6. Linear Quadratic Optimal Control Problems

1. Introduction

2. The Deterministic LQ Problems Revisited

2.1. Formulation

2.2. A minimization problem of a quadratic functional

2.3. A linear Hamiltonian system

2.4. The Riccati equation and feedback optimal control

3. FormuLation of Stochastic LQ Problems

3.1. Statement of the problems

3.2. Examples

4. Finiteness and Solvability

5. A Necessary Condition and a Hamiltonian System

6. Stochastic Riceati Equations

7. GLobal Solvability of Stochastic Riccati EQuations

7.1. Existence: Thc standard case

7.2. Existence: The case C = 0, S = 0, and Q,G >_ 0

7.3. Existence: The one-dimensional case

8. A Mean-variance Portfolio Selection Problem

9. Historical Remarks

Chapter 7. Backward Stochastic Differential Equations

1. Introduction

2. Linear Backward Stochastic Differential EQuations

3. Nonlinear Backward Stochastic Differential Equations

3.1. BSDEs in finite deterministic durations: Method of

contraction mapping

3.2. BSDEs in random durations: Method of continuation

4. Feynman-Kac-Type Formulae

4.1. Representation via SDEs

4.2. Representation via BSDEs

5. Forward-Backward Stochastic Differential Equations

5.1. General formulation and nonsolvability

5.2. The four-step scheme, a heuristic derivation

5.3. Several solvable classes of FBSDEs

6. Option Pricing Problems

6.1. European call options and the Black-Scholes formula

6.2. Other options

7. Historical Remarks

References

Index

内容摘要:

随机控制也叫试探控制,是最原始的控制方式,是其他一切控制方式的基础。随机控制是完全建立在偶然机遇的基础上,是“试试看”思想在控制活动中的体现。随机控制在成功的同时,常常伴随着失败。这种控制方式有较大的风险,对事关重大的活动,一般不宜采用这种控制方式。 《随机控制》(作者雍炯敏)是关于介绍随机控制的英文教材。

书籍规格:

书籍详细信息
书名随机控制站内查询相似图书
9787510048029
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出版地北京出版单位世界图书出版公司北京公司
版次影印本印次1
定价(元)68.0语种英文
尺寸23 × 15装帧平装
页数 468 印数

书籍信息归属:

随机控制是世界图书出版公司北京公司于2012.6出版的中图分类号为 O231 的主题关于 随机控制-英文 的书籍。