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Lévy Matters V

Functionals of Lévy Processes

  • Book
  • © 2015

Overview

Authors:
  1. Lars Nørvang Andersen

    1. Department of Mathematics, Aarhus University, Aarhus, Denmark

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  2. Søren Asmussen

    1. Department of Mathematics, Aarhus University, Aarhus, Denmark

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  3. Frank Aurzada

    1. Fachbereich Mathematik, Technische Universität Darmstadt, Darmstadt, Germany

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  4. Peter W. Glynn

    1. Dept of Management Science & Engineering, Stanford University, Stanford, USA

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  5. Makoto Maejima

    1. Department of Mathematics, Keio University, Yokohama, Japan

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  6. Mats Pihlsgård

    1. Faculty of Medicine, Lund University, Lund, Sweden

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  7. Thomas Simon

    1. Laboratoire Paul Painlevé, Université de Lille 1, Villeneuve d’Ascq Cedex, France

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

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

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Table of contents (3 chapters)

  1. Front Matter

    Pages i-xvi
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  2. Classes of Infinitely Divisible Distributions and Examples

    • Makoto Maejima
    Pages 1-65

  3. Lévy Processes with Two-Sided Reflection

    • Lars Nørvang Andersen, Søren Asmussen, Peter W. Glynn, Mats Pihlsgård
    Pages 67-182

  4. Persistence Probabilities and Exponents

    • Frank Aurzada, Thomas Simon
    Pages 183-224

  5. Back Matter

    Pages 225-226
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, Aarhus University, Aarhus, Denmark

    Lars Nørvang Andersen, Søren Asmussen

  • Fachbereich Mathematik, Technische Universität Darmstadt, Darmstadt, Germany

    Frank Aurzada

  • Dept of Management Science & Engineering, Stanford University, Stanford, USA

    Peter W. Glynn

  • Department of Mathematics, Keio University, Yokohama, Japan

    Makoto Maejima

  • Faculty of Medicine, Lund University, Lund, Sweden

    Mats Pihlsgård

  • Laboratoire Paul Painlevé, Université de Lille 1, Villeneuve d’Ascq Cedex, France

    Thomas Simon

Bibliographic Information

  • Book Title: Lévy Matters V

  • Book Subtitle: Functionals of Lévy Processes

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

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-319-23138-9

  • Publisher: Springer Cham

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

  • Copyright Information: Springer International Publishing Switzerland 2015

  • Softcover ISBN: 978-3-319-23137-2Published: 05 November 2015

  • eBook ISBN: 978-3-319-23138-9Published: 24 October 2015

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XVI, 224

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

  • Topics: Probability Theory and Stochastic Processes

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