Lévy过程

Preface

0 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 Levy Processes as Markov Processes

1 Levy 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 Levy 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

Vll Levy 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

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