图书介绍
Stochastic differential equations: an introduction with applications Sixth Edition = 随机微分方程 第6版PDF|Epub|txt|kindle电子书版本网盘下载
- Bernt Oksendal 著
- 出版社： Springer ; 世界图书出版公司
- ISBN：750627308X
- 出版时间：2006
- 标注页数：372页
- 文件大小：34MB
- 文件页数：403页
- 主题词：随机微分方程－研究生－教材－英文
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Stochastic differential equations: an introduction with applications Sixth Edition = 随机微分方程 第6版PDF格式电子书版下载
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图书目录
1 Introduction1
1.1 Stochastic Analogs of Classical Differential Equations1
1.2 Filtering Problems2
1.3 Stochastic Approach to Deterministic Boundary Value Problems3
1.4 Optimal Stopping3
1.5 Stochastic Control4
1.6 Mathematical Finance4
2 Some Mathematical Preliminaries7
2.1 Probability Spaces，Random Variables and Stochastic Processes7
2.2 An Important Example：Brownian Motion12
Exercises15
3 Ito Integrals21
3.1 Construction of the Ito Integral21
3.2 Some properties of the Ito integral30
3.3 Extensions of the Ito integral34
Exercises37
4 The Ito Formula and the Martingale Representation Theorem43
4.1 The 1-dimensional Ito formula43
4.2 The Multi-dimensional Ito Formula48
4.3 The Martingale Representation Theorem49
Exercises54
5 Stochastic Differential Equations63
5.1 Examples and Some Solution Methods63
5.2 An Existence and Uniqueness Result68
5.3 Weak and Strong Solutions72
Exercises74
6 The Filtering Problem83
6.1 Introduction83
6.2 The 1-Dimensional Linear Filtering Problem85
6.3 The Multidimensional Linear Filtering Problem104
Exercises105
7 Diffusions：Basic Properties113
7.1 The Markov Property113
7.2 The Strong Markov Property116
7.3 The Generator of an Ito Diffusion121
7.4 The Dynkin Formula124
7.5 The Characteristic Operator126
Exercises128
8 Other Topics in Diffusion Theory139
8.1 Kolmogorov’s Backward Equation.The Resolvent139
8.2 The Feynman-Kac Formula.Killing143
8.3 The Martingale Problem146
8.4 When is an Ito Process a Diffusion？148
8.5 Random Time Change153
8.6 The Girsanov Theorem159
Exercises168
9 Applications to Boundary Value Problems175
9.1 The Combined Dirichlet-Poisson Problem.Uniqueness175
9.2 The Dirichlet Problem.Regular Points179
9.3 The Poisson Problem190
Exercises197
10 Application to Optimal Stopping205
10.1 The Time-Homogeneous Case205
10.2 The Time-Inhomogeneous Case218
10.3 Optimal Stopping Problems Involving an Integral222
10.4 Connection with Variational Inequalities224
Exercises228
11 Application to Stochastic Control235
11.1 Statement of the Problem235
11.2 The Hamilton-Jacobi-Bellman Equation237
11.3 Stochastic control problems with terminal conditions251
Exercises252
12 Application to Mathematical Finance261
12.1 Market，portfolio and arbitrage261
12.2 Attainability and Completeness271
12.3 Option Pricing278
Exercises298
Appendix A：Normal Random Variables305
Appendix B：Conditional Expectation309
Appendix C：Uniform Integrability and Martingale Convergence311
Appendix D：An Approximation Result315
Solutions and Additional Hints to Some of the Exercises319
References349
List of Frequently Used Notation and Symbols357
Index361