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 livy processes and the levy-khintchine formula

2 markov property and related operators

3 absolutely continuous resolvents

4 transience and recurrence

5 exercises

6 comments

2 elements of potential theory

ii 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 subordinotors

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

vii 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