Fluctuation theory for Lévy processes. Ecole d'Eté de probabilités de Saint-Flour XXXV -- 2005.
type: Item
instance of: scholarly article
title: Fluctuation theory for Lévy processes. Ecole d'Eté de probabilités de Saint-Flour XXXV -- 2005.
zbMATH Open document ID: 1128.60036
DOI: 10.1007/978-3-540-48511-7
published in: Lecture Notes in Mathematics
publication date: 2007-05-09T00:00:00Z
review text: The present note is based on a series of lectures given by the author at the 35th summer school in probability at Saint-Flour in July 2005. This note is devoted to some interesting recent developments within the theory of Lévy processes. It consists of 10 sections. The first four chapters contain a short introduction into the general theory. For example, the Lévy-Itô decomposition is presented, subordinators are introduced, their special properties are treated and, furthermore, it deals with local times and excursions, with the ladder process as well as with the Wiener-Hopf factorization of Lévy processes. Section 5 presents recent further developments of the latter factorization, while section 6 is devoted to creeping and related questions. Section 7 deals with Spitzer's condition for Lévy processes and random walks. The solution of a basic question about that condition (due to J. Bertoin and the author) is given. Section 8 treats Lévy processes conditioned to stay positive, while sections 9 and 10 deal with spectrally negative Lévy processes and the small-time behavior, respectively. The presentation in this note is very clear; every section starts with a short introduction into its topic. In most cases the author motivates the properties of Lévy processes by the corresponding ones for random walks. To read this note a basic knowledge about Lévy processes is necessary.
reviewed by: Werner Linde
Mathematics Subject Classification ID: 60G51
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 60G55
Mathematics Subject Classification ID: 60J55
Mathematics Subject Classification ID: 60K15
zbMATH DE Number: 5150952
zbMATH Keywords: Levy process
zbMATH Keywords: random walk
zbMATH Keywords: Wiener-Hopf factorization
zbMATH Keywords: ladder process
author: Ronald A. Doney
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-540-48511-7
OpenAlex ID: W4206817348
description: scientific article; zbMATH DE number 5150952