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Lévy Matters V

Functionals of Lévy Processes

  • Lars Nørvang Andersen
  • Søren Asmussen
  • Frank Aurzada
  • Peter W. Glynn
  • Makoto Maejima
  • Mats Pihlsgård
  • Thomas Simon

Part of the Lecture Notes in Mathematics book series (LNM, volume 2149)

Also part of the Lévy Matters book sub series (LEVY, volume 2149)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Lars Nørvang Andersen, Søren Asmussen, Peter W. Glynn, Mats Pihlsgård
    Pages 67-182
  3. Frank Aurzada, Thomas Simon
    Pages 183-224
  4. Back Matter
    Pages 225-226

About this book

Introduction

This three-chapter volume concerns the distributions of certain functionals of Lévy processes. The first chapter, by Makoto Maejima, surveys representations of the main sub-classes of infinitesimal distributions in terms of mappings of certain Lévy processes via stochastic integration. The second chapter, by Lars Nørvang Andersen, Søren Asmussen, Peter W. Glynn and Mats Pihlsgård, concerns Lévy processes reflected at two barriers, where reflection is formulated à la Skorokhod. These processes can be used to model systems with a finite capacity, which is crucial in many real life situations, a most important quantity being the overflow or the loss occurring at the upper barrier.  If a process is killed when crossing the boundary, a natural question concerns its lifetime. Deep formulas from fluctuation theory are the key to many classical results, which are reviewed in the third chapter by Frank Aurzada and Thomas Simon. The main part, however, discusses recent advances and developments in the setting where the process is given either by the partial sum of a random walk or the integral of a Lévy process.

 

Keywords

60E07,60G18,60G51,60K20,60K35 First passage problem, Infinitely divisible distribution, Reflected Lévy process, Self-similar Lévy process Selfdecomposable distribution,

Authors and affiliations

  • Lars Nørvang Andersen
    • 1
  • Søren Asmussen
    • 2
  • Frank Aurzada
    • 3
  • Peter W. Glynn
    • 4
  • Makoto Maejima
    • 5
  • Mats Pihlsgård
    • 6
  • Thomas Simon
    • 7
  1. 1.Department of MathematicsAarhus UniversityAarhusDenmark
  2. 2.Department of MathematicsAarhus UniversityAarhusDenmark
  3. 3.Fachbereich MathematikTechnische Universität DarmstadtDarmstadtGermany
  4. 4.Dept of Management Science & EngineeringStanford UniversityStanfordUSA
  5. 5.Department of MathematicsKeio UniversityYokohamaJapan
  6. 6.Faculty of MedicineLund UniversityLundSweden
  7. 7.Laboratoire Paul PainlevéUniversité de Lille 1Villeneuve d’Ascq CedexFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-23138-9
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-23137-2
  • Online ISBN 978-3-319-23138-9
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site