Stochastic differential equations: an introduction with applications Sixth Edition = 随机微分方程 第6版pdf电子书版本下载

点此进入-本书在线PDF格式电子书下载【推荐-云解压-方便快捷】直接下载PDF格式图书。移动端-PC端通用
种子下载[BT下载速度快] 温馨提示：（请使用BT下载软件FDM进行下载）软件下载地址页 直链下载[便捷但速度慢]   [在线试读本书]   [在线获取解压码]

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

下载的文件为RAR压缩包。需要使用解压软件进行解压得到PDF格式图书。

建议使用BT下载工具Free Download Manager进行下载,简称FDM(免费,没有广告,支持多平台）。本站资源全部打包为BT种子。所以需要使用专业的BT下载软件进行下载。如 BitComet qBittorrent uTorrent等BT下载工具。迅雷目前由于本站不是热门资源。不推荐使用！后期资源热门了。安装了迅雷也可以迅雷进行下载！

（文件页数 要大于 标注页数，上中下等多册电子书除外）

注意：本站所有压缩包均有解压码： 点击下载压缩包解压工具

1 Introduction 1

1.1 Stochastic Analogs of Classical Differential Equations 1

1.2 Filtering Problems 2

1.3 Stochastic Approach to Deterministic Boundary Value Problems 3

1.4 Optimal Stopping 3

1.5 Stochastic Control 4

1.6 Mathematical Finance 4

2 Some Mathematical Preliminaries 7

2.1 Probability Spaces，Random Variables and Stochastic Processes 7

2.2 An Important Example：Brownian Motion 12

Exercises 15

3 Ito Integrals 21

3.1 Construction of the Ito Integral 21

3.2 Some properties of the Ito integral 30

3.3 Extensions of the Ito integral 34

Exercises 37

4 The Ito Formula and the Martingale Representation Theorem 43

4.1 The 1-dimensional Ito formula 43

4.2 The Multi-dimensional Ito Formula 48

4.3 The Martingale Representation Theorem 49

Exercises 54

5 Stochastic Differential Equations 63

5.1 Examples and Some Solution Methods 63

5.2 An Existence and Uniqueness Result 68

5.3 Weak and Strong Solutions 72

Exercises 74

6 The Filtering Problem 83

6.1 Introduction 83

6.2 The 1-Dimensional Linear Filtering Problem 85

6.3 The Multidimensional Linear Filtering Problem 104

Exercises 105

7 Diffusions：Basic Properties 113

7.1 The Markov Property 113

7.2 The Strong Markov Property 116

7.3 The Generator of an Ito Diffusion 121

7.4 The Dynkin Formula 124

7.5 The Characteristic Operator 126

Exercises 128

8 Other Topics in Diffusion Theory 139

8.1 Kolmogorov’s Backward Equation.The Resolvent 139

8.2 The Feynman-Kac Formula.Killing 143

8.3 The Martingale Problem 146

8.4 When is an Ito Process a Diffusion？ 148

8.5 Random Time Change 153

8.6 The Girsanov Theorem 159

Exercises 168

9 Applications to Boundary Value Problems 175

9.1 The Combined Dirichlet-Poisson Problem.Uniqueness 175

9.2 The Dirichlet Problem.Regular Points 179

9.3 The Poisson Problem 190

Exercises 197

10 Application to Optimal Stopping 205

10.1 The Time-Homogeneous Case 205

10.2 The Time-Inhomogeneous Case 218

10.3 Optimal Stopping Problems Involving an Integral 222

10.4 Connection with Variational Inequalities 224

Exercises 228

11 Application to Stochastic Control 235

11.1 Statement of the Problem 235

11.2 The Hamilton-Jacobi-Bellman Equation 237

11.3 Stochastic control problems with terminal conditions 251

Exercises 252

12 Application to Mathematical Finance 261

12.1 Market，portfolio and arbitrage 261

12.2 Attainability and Completeness 271

12.3 Option Pricing 278

Exercises 298

Appendix A：Normal Random Variables 305

Appendix B：Conditional Expectation 309

Appendix C：Uniform Integrability and Martingale Convergence 311

Appendix D：An Approximation Result 315

Solutions and Additional Hints to Some of the Exercises 319

References 349

List of Frequently Used Notation and Symbols 357

Index 361