Lévy Matters II

Recent Progress in Theory and Applications: Fractional Lévy Fields, and Scale Functions

  • Serge Cohen
  • Alexey Kuznetsov
  • Andreas E. Kyprianou
  • Victor Rivero

Part of the Lecture Notes in Mathematics book series (LNM, volume 2061)

Also part of the Lévy Matters book sub series (LEVY, volume 2061)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Serge Cohen
    Pages 1-95
  3. Alexey Kuznetsov, Andreas E. Kyprianou, Victor Rivero
    Pages 97-186
  4. Back Matter
    Pages 187-188

About this book


This is the second volume in a subseries of the Lecture Notes in Mathematics called Lévy Matters, which is published at irregular intervals over the years. Each volume examines a number of key topics in the theory or applications of Lévy processes and pays tribute to the state of the art of this rapidly evolving subject with special emphasis on the non-Brownian world.
The expository articles in this second volume cover two important topics in the area of Lévy processes.
The first article by Serge Cohen reviews the most
important findings on fractional Lévy fields to date in a self-contained piece, offering a theoretical introduction as well as possible applications and simulation techniques.
The second article, by Alexey Kuznetsov, Andreas E. Kyprianou, and Victor Rivero, presents an up to date account of the theory and application of scale functions for spectrally negative Lévy processes, including an extensive numerical overview.


60G10, 60G40, 60G51, 60G70, 60J10, 60J45 excursion theory for Lévy processes fluctuation theory for subordinators fractional Lévy field scale functions for subordinators

Authors and affiliations

  • Serge Cohen
    • 1
  • Alexey Kuznetsov
    • 2
  • Andreas E. Kyprianou
    • 3
  • Victor Rivero
    • 4
  1. 1.Institut Mathématique de ToulouseUniversité Paul SabatierToulouse Cedex 4France
  2. 2.Department of Mathematics and StatisticsYork UniversityTorontoCanada
  3. 3.Department of Mathematical SciencesUniversity of BathBathUnited Kingdom
  4. 4.CIMAT A.C.GuanajuatoMexico

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2013
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-31406-3
  • Online ISBN 978-3-642-31407-0
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site