随机微分方程
随机微分方程
图书信息
书名：随机微分方程
出版社: 世界图书出管社; 第1版 (2006年11月1日)
平装: 365页
开本: 24开
isbn: 750627308x
条形码: 9787506273084
商品尺寸: 22.5 x 15 x 1.6 cm
商品重量: 422 g
品牌: 世界图书出版公司北京公司
内容简介
《随机微分方程》(第6版)是《Universitext》丛书之一，是一部理想的研究生教材，内容做了较大的修改和补充，包括鞅表示论、变分不等式和随机控制等内容，书后附有部分习题解答和提示。随机微分方程在数学以外的许多领域有着广泛的应用，它对数学领域中的许多分支起着有效的联结作用。
作者简介
作者：(挪)科森多尔
目录
Introduction
1.1 Stochastic Analogs of Classical Differential Equations
1.2 Filtering Problems
1.3 Stochastic Approach to Deterministic Boundary Value Problems
1.4 Optimal Stopping
1.5 Stochastic Control
1.6 Mathematical Finance
Some Mathematical Preliminaries
2.1 Probability Spaces, Random Variables and Stochastic Processes
2.2 An Important Example: Brownian Motion
Exercises
Ito Integrals
3.1 Construction of the It5 Integral
3.2 Some properties of the It5 integral
3.3 Extensions of the Ito integral
Exercises
The Ito Formula and the Martingale Representation
Theorem
4.1 The 1-dimensional It5 formula
4.2 The Multi-dimensional It5 Formula
4.3 The Martingale Representation Theorem
Exercises
Stochastic Differential Equations
5.1 Examples and Some Solution Methods
5.2 An Existence and Uniqueness Result
5.3 Weak and Strong Solutions
Exercises
6 The Filtering Problem
6.1 Introduction
6.2 The 1-Dimensional Linear Filtering Problem
6.3 The Multidimensional Linear Filtering Problem
Exercises
7 Diffusions: Basic Properties
7.1 The Markov Property
7.2 The Strong Markov Property
7.3 The Generator of an It5 Diffusion
7.4 The Dynkin Formula
7.5 The Characteristic Operator
Exercises
8 Other Topics in Diffusion Theory
8.1 Kolmogorov''s Backward Equation. The Resolvent
8.2 The Feynman-Kac Formula. Killing
8.3 The Martingale Problem
8.4 When is an It5 Process a Diffusion?
8.5 Random Time Change
8.6 The Girsanov Theorem
Exercises
9 Applications to Boundary Value Problems
9.1 The Combined Dirichlet-Poisson Problem. Uniqueness
9.2 The Dirichlet Problem. Regular Points
9.3 The Poisson Problem
Exercises
10 Application to Optimal Stopping
10.1 The Time-Homogeneous Case
10.2 The Time-Inhomogeneous Case
10.3 Optimal Stopping Problems Involving an Integral
10.4 Connection with Variational Inequalities
Exercises
11 Application to Stochastic Control
11.1 Statement of the Problem
11.2 The Ha.milton-Jacobi-Bellman Equation
11.3 Stochastic control problems with terminal conditions
Exercises
12 Application to Mathematical Finance
12.1 Market, portfolio and arbitrage
12.2 Attainability and Completeness
12.3 Option Pricing
Exercises
Appendix A: Normal Random Variables
Appendix B: Conditional Expectation
Appendix C: Uniform Integrability and Martingale
Convergence
Appendix D: An Approximation Result
Solutions and Additional Hints to Some of the Exercises..
References
List of Frequently Used Notation and Symbols
Index