本書是一部全新、綜合描述Lévy過程理論的教程。近年來，Lévy過程理論作為現代概率的重要一支得到了迅速的發展，在序列、數學金融和風險估計等各個領域的應用廣泛。Bertoin教授運用概率結構和分析工具之間強有力的聯繫將這個核心理論講述的相當簡明。介紹從屬過程的特殊性質以及其在研究實值Lévy過程和起伏理論時的關鍵特征。詳盡講述了沒有正跳躍的Lévy過程和平穩過程。

Preface
O Preliminaries
1 Notation
2 Infinitely divisible distributions
3 Martingales
4 Poisson processes
5 Poisson measures and Poisson point processes
6 Brownian motion
7 Regular variation and Tauberian theorems
Ⅰ Lévy Processes as Markov Processes
1 Lévy processes and the Lbvy-Khintchine formula
2 Markov property and related operators
3 Absolutely continuous resoivents
4 Transience and recurrence
5 Exercises
6 Comments
Ⅱ Elements of Potential Theory
1 Duality and time reversal
2 Capacitary measure
3 Essentially polar sets and capacity
4 Energy
5 The case of a single point
6 Exercises
7 Comments
Ⅲ Subordimtors
1 Definitions and first properties
2 Passage across a level
3 The arcsine laws
4 Rates of growth
5 Dimension of the range
6 Exercises
7 Comments
Ⅳ Local Time and Excursions of a Markov Process
1 Framework
2 Construction of the local time
3 Inverse local time
4 Excursion measure and excursion process
5 The cases of holding points and of irregular points
6 Exercises
7 Comments
Ⅴ Local Times of a Lévy Process
1 Occupation measure and local times
2 Hilbert transform of local times
3 Jointly continuous local times
4 Exercises
5 Comments
Ⅵ Fluctuation Theory
1 The reflected process and the ladder process
2 Fluctuation identities
3 Some applications of the ladder time process
4 Some applications of the ladder height process
5 Increase times
6 Exercises
7 Comments
Ⅶ Lévy Processes with no Positive Jumps
1 Fluctuation theory with no positive jumps
2 The scale function
3 The process conditioned to stay positive
4 Some path transformations
5 Exercises
6 Comments
Ⅷ Stable Processes and the Scaling Property
1 Definition and probability estimates
2 Some sample path properties
3 Bridges
4 Normalized excursion and meander
5 Exercises
6 Comments
References
List of symbols
Index