Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Some elements on Lévy processes


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:

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