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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