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随机积分导论  第2版
随机积分导论  第2版

随机积分导论 第2版PDF电子书下载

数理化

  • 电子书积分:11 积分如何计算积分?
  • 作 者:(美)钟开莱(Chung K. L.),R. J. Williams著
  • 出 版 社:北京/西安:世界图书出版公司出版社
  • 出版年份:2014
  • ISBN:9787510070259
  • 页数:277 页
图书介绍:本书是一部可读性很强的讲述随机积分和随机微分方程的入门教程。将基本理论和应用巧妙结合,非常适合学习过概率论知识的研究生,学习随机积分。运用现代方法,随机积分的定义是为了可料被积函数和局部鞅,紧接着是连续鞅的变分公式ITO变化。书中包括在布朗运动的描述、鞅的Hermite多项式、Feynman-Kac泛函和Schrodinger方程。这是第二版,讨论了Cameron-Martin-Giranov变换,并且在最后一章引入随机微分方程和一些学生用的练习。读者对象:数学专业、概论论、随机统计等学科的研。
《随机积分导论 第2版》目录
标签:导论 积分

1.PRELIMINARIES 1

1.1 Notations and Conventions 1

1.2 Measurability,Lp Spaces and Monotone Class Theorems 2

1.3 Functions of Bounded Variation and Stieltjes Integrals 4

1.4 Probability Space,Random Variables,Filtration 6

1.5 Convergence,Conditioning 7

1.6 Stochastic Processes 8

1.7 Optional Times 9

1.8 Two Canonical Processes 10

1.9 Martingales 13

1.10 Local Martingales 18

1.11 Exercises 21

2.DEFINITION OF THE STOCHASTIC INTEGRAL 23

2.1 Introduction 23

2.2 Predictable Sets and Processes 25

2.3 Stochastic Intervals 26

2.4 Measure on the Predictable Sets 32

2.5 Definition of the Stochastic Integral 34

2.6 Extension to Local Integrators and Integrands 43

2.7 Substitution Formula 48

2.8 A Sufficient Condition for Extendability of λz 50

2.9 Exercises 54

3.EXTENSION OF THE PREDICTABLE INTEGRANDS 57

3.1 Introduction 57

3.2 Relationship between P,O,and Adapted Processes 57

3.3 Extension of the Integrands 63

3.4 A Historical Note 71

3.5 Exercises 73

4.QUADRATIC VARIATION PROCESS 75

4.1 Introduction 75

4.2 Definition and Characterization of Quadratic Variation 75

4.3 Properties of Quadratic Variation for an L2-martingale 79

4.4 Direct Definition of μM 82

4.5 Decomposition of(M)2 86

4.6 A Limit Theorem 89

4.7 Exercises 90

5.THE ITO FORMULA 93

5.1 Introduction 93

5.2 One-dimensional It? Formula 94

5.3 Mutual Variation Process 99

5.4 Multi-dimensional It? Formula 109

5.5 Exercises 112

6.APPLICATIONS OF THE ITO FORMULA 117

6.1 Characterization of Brownian Motion 117

6.2 Exponential Processes 120

6.3 A Family of Martingales Generated by M 123

6.4 Feynman-Kac Functional and the Schr?dinger Equation 128

6.5 Exercises 136

7.LOCAL TIME AND TANAKA'S FORMULA 141

7.1 Introduction 141

7.2 Local Time 142

7.3 Tanaka's Formula 150

7.4 Proof of Lemma 7.2 153

7.5 Exercises 155

8.REFLECTED BROWNIAN MOTIONS 157

8.1 Introduction 157

8.2 Brownian Motion Reflected at Zero 158

8.3 Analytical Theory of Z via the It? Formula 161

8.4 Approximations in Storage Theory 163

8.5 Reflected Brownian Motions in a Wedge 174

8.6 Alternative Derivation of Equation(8.7) 178

8.7 Exercises 181

9.GENERALIZED ITO FORMULA,CHANGE OF TIME AND MEASURE 183

9.1 Introduction 183

9.2 Generalized It? Formula 184

9.3 Change of Time 187

9.4 Change of Measure 197

9.5 Exercises 214

10.STOCHASTIC DIFFERENTIAL EQUATIONS 217

10.1 Introduction 217

10.2 Existence and Uniqueness for Lipschitz Coefficients 220

10.3 Strong Markov Property of the Solution 235

10.4 Strong and Weak Solutions 243

10.5 Examples 252

10.6 Exercises 262

REFERENCES 265

INDEX 273

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