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Levy过程  英文版
Levy过程  英文版

Levy过程 英文版PDF电子书下载

数理化

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  • 作 者:JeanBertoin著
  • 出 版 社:世界图书北京出版公司
  • 出版年份:2010
  • ISBN:9787510005091
  • 页数:266 页
图书介绍:本书是一部最新、最综合描述Lévy过程理论的教程。近年来,Lévy过程作为现代概率的重要一支得到了迅速的发展,在序列、数学金融和风险估计等各个领域的应用广泛。Bertoin教授运用概率结构和分析工具之间强有力的联系将这个核心理论讲述的相当简明。
《Levy过程 英文版》目录
标签:英文版 过程

0 Preliminaries 1

1 Notation 1

2 Infinitely divisible distributions 2

3 Martingales 3

4 Poisson processes 4

5 Poisson measures and Poisson point processes 6

6 Brownian motion 8

7 Regular variation and Tauberian theorems 9

Ⅰ Lévy Processes as Markov Processes 11

1 Lévy processes and the Lévy-Khintchine formula 11

2 Markov property and related operators 18

3 Absolutely continuous resolvents 24

4 Transience and recurrence 31

5 Exercises 39

6 Comments 41

Ⅱ Elements of Potential Theory 43

1 Duality and time reversal 43

2 Capacitary measure 48

3 Essentially polar sets and capacity 53

4 Energy 56

5 The case of a single point 61

6 Exercises 68

7 Comments 70

Ⅲ Subordinators 71

1 Definitions and first properties 71

2 Passage across a level 75

3 The arcsine laws 81

4 Rates of growth 84

5 Dimension of the range 93

6 Exercises 99

7 Comments 100

Ⅳ Local Time and Excursions of a Markov Process 103

1 Framework 103

2 Construction of the local time 105

3 Inverse local time 112

4 Excursion measure and excursion process 116

5 The cases of holding points and of irregular points 121

6 Exercises 123

7 Comments 124

Ⅴ Local Times of a Lévy Process 125

1 Occupation measure and local times 125

2 Hilbert transform of local times 134

3 Jointly continuous local times 143

4 Exercises 150

5 Comments 153

Ⅵ Fluctuation Theory 155

1 The reflected process and the ladder process 155

2 Fluctuation identities 159

3 Some applications of the ladder time process 166

4 Some applications of the ladder height process 171

5 Increase times 176

6 Exercises 182

7 Comments 184

Ⅶ Lévy Processes with no Positive Jumps 187

1 Fluctuation theory with no positive jumps 187

2 The scale function 194

3 The process conditioned to stay positive 198

4 Some path transformations 206

5 Exercises 212

6 Comments 214

Ⅷ Stable Processes and the Scaling Property 216

1 Definition and probability estimates 216

2 Some sample path properties 222

3 Bridges 226

4 Normalized excursion and meander 232

5 Exercises 237

6 Comments 240

References 242

List of symbols 261

Index 264

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