### Some elements on Lévy processes

**Auteur(s): **

**Ce document est publié dans:**
* Stochastic Processes: Modelling and Simulation. Theory and Methods.* Handbook of Statistics 20. North Holland. * (to appear) *
**Code(s) de Classification MSC:**

- 60J30 Processes with independent increments

**Résumé:** The purpose of this text is to provide a brief survey of some
of the most salient features of the theory. We will first
present the fundamental aspects of Lévy processes
(Markov property and infinite divisibility) and describe
the probabilistic structure. Then we will dwell on
techniques used to derive the distribution of certain
important functionals of Lévy processes. The
final section is devoted to some remarkable sample path
properties such as transience or recurrence, information
on the rate of growth, and certain geometric properties
of the range.

**Mots Clés:** *Levy processes*

**Date:** 1999-02-04

**Prépublication numéro:** *PMA-485*