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Lévy Matters II

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

  • Over the past 10-15 years, we have seen a revival of general Lévy processes theory as well as a burst of new applications

  • There is a lively and growing research community in this area

  • Expository articles help to disseminate important theoretical and applied research to other researchers and in particular to young researchers like PhD students and Postdocs

  • Chapters attract different focus groups of readers

  • Includes supplementary material: sn.pub/extras

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

Part of the book sub series: Lévy Matters (LEVY)

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Table of contents (2 chapters)

  1. Front Matter

    Pages i-xii
  2. Fractional Lévy Fields

    • Serge Cohen
    Pages 1-95
  3. The Theory of Scale Functions for Spectrally Negative Lévy Processes

    • 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.

Keywords

  • 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

  • Institut Mathématique de Toulouse, Université Paul Sabatier, Toulouse Cedex 4, France

    Serge Cohen

  • Department of Mathematics and Statistics, York University, Toronto, Canada

    Alexey Kuznetsov

  • Department of Mathematical Sciences, University of Bath, Bath, United Kingdom

    Andreas E. Kyprianou

  • CIMAT A.C., Guanajuato, Mexico

    Victor Rivero

Bibliographic Information

  • Book Title: Lévy Matters II

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

  • Authors: Serge Cohen, Alexey Kuznetsov, Andreas E. Kyprianou, Victor Rivero

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-642-31407-0

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2013

  • Softcover ISBN: 978-3-642-31406-3Published: 11 September 2012

  • eBook ISBN: 978-3-642-31407-0Published: 14 September 2012

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XII, 186

  • Number of Illustrations: 7 b/w illustrations, 1 illustrations in colour

  • Topics: Mathematics, Probability Theory

Buying options

eBook USD 34.99
Price excludes VAT (Canada)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions