Lévy Matters

Lévy Matters V

Functionals of Lévy Processes

Authors: Andersen, L.N., Asmussen, S., Aurzada, F., Glynn, P.W., Maejima, M., Pihlsgård, M., Simon, Th.

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  • ISBN 978-3-319-23138-9
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Softcover $59.99
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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.

Table of contents (3 chapters)

  • Classes of Infinitely Divisible Distributions and Examples

    Maejima, Makoto

    Pages 1-65

  • Lévy Processes with Two-Sided Reflection

    Andersen, Lars Nørvang (et al.)

    Pages 67-182

  • Persistence Probabilities and Exponents

    Aurzada, Frank (et al.)

    Pages 183-224

Buy this book

eBook $44.99
price for USA in USD (gross)
  • ISBN 978-3-319-23138-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA in USD
  • ISBN 978-3-319-23137-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Lévy Matters V
Book Subtitle
Functionals of Lévy Processes
Authors
Series Title
Lévy Matters
Series Volume
2149
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-23138-9
DOI
10.1007/978-3-319-23138-9
Softcover ISBN
978-3-319-23137-2
Series ISSN
2190-6637
Edition Number
1
Number of Pages
XVI, 224
Number of Illustrations and Tables
1 b/w illustrations, 7 illustrations in colour
Topics