Lévy processes

✍ Scribed by Jean Bertoin

• Publisher: Cambridge University Press
• Year: 1996
• Tongue: English
• Leaves: 275
• Series: Cambridge Tracts in Mathematics; 121
• Category: Library

✦ Table of Contents

Cover......Page 1
Title page......Page 2
Preface......Page 7
1 Notation......Page 10
2 lnfinitely divisible distributions......Page 11
3 Martingales......Page 12
4 Poisson processes......Page 13
5 Poisson measures and Poisson point processes......Page 15
6 Brownian motion......Page 17
7 Regular variation and Tauberian theorems......Page 18
1 Lévy processes and the Lévy-Khintchine formula......Page 20
2 Markov property and related operators......Page 27
3 Absolutely continuous resolvents......Page 33
4 Transience and recurrence......Page 40
5 Exercises......Page 48
6 Comments......Page 50
1 Duality and time reversai......Page 52
2 capacitary measure......Page 57
3 Essentially polar sets and capacity......Page 62
4 Energy......Page 65
5 The case of a single point......Page 70
6 Exercises......Page 77
7 Comments......Page 79
1 Definitions and first properties......Page 80
2 Passage across a level......Page 84
3 The arcsine laws......Page 90
4 Rates of growth......Page 93
5 Dimension of the range......Page 102
6 Exercises......Page 108
7 Comments......Page 109
1 Framework......Page 112
2 Construction of the local time......Page 114
3 Inverse local time......Page 121
4 Excursion measure and excursion process......Page 125
5 The cases of holding points and of irregular points......Page 130
6 Exercises......Page 132
7 Comments......Page 133
1 Occupation measure and local times......Page 134
2 Hilbert transform of local times......Page 143
3 Jointly continuous local times......Page 152
4 Exercises......Page 159
5 Comments......Page 162
1 The reflected process and the ladder process......Page 164
2 Fluctuation identities......Page 168
3 Some applications of the ladder time process......Page 175
4 Some applications of the ladder height process......Page 180
5 Increase times......Page 185
6 Exercises......Page 191
7 Comments......Page 193
1 Fluctuation theory with no positive jumps......Page 196
2 The scale function......Page 203
3 The process conditioned to stay positive......Page 207
4 Some path transformations......Page 215
5 Exercises......Page 221
6 Comments......Page 223
1 Definition and probability estimates......Page 225
2 Some sample path properties......Page 231
3 Bridges......Page 235
4 Normalized excursion and meander......Page 241
5 Exercises......Page 246
6 Comments......Page 249
References......Page 251
List of symbols......Page 270
Index......Page 273