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Lévy matters. V, Functionals of Lévy processes

Author: Lars Nørvang AndersenSøren AsmussenFrank AurzadaPeter W GlynnMakoto MaejimaAll authors
Publisher: Cham : Springer, [2015] ©2015
Series: Lecture notes in mathematics (Springer-Verlag), 2149.; Lévy matters, 5.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:
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  Read more...
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Additional Physical Format: Online version:
Lévy matters V.
Cham : Springer, 2015
(OCoLC)932168693
(GyWOH)har150452900
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Lars Nørvang Andersen; Søren Asmussen; Frank Aurzada; Peter W Glynn; Makoto Maejima; Mats Pihlsgård; Thomas Simon, (Mathematician)
ISBN: 9783319231372 3319231375 3319231383 9783319231389
OCLC Number: 930610629
Description: xvi, 224 pages : illustrations (chiefly color) ; 24 cm.
Contents: Classes of Infinitely Divisible Distributions and Examples --
Lévy Processes with Two-Sided Reflection --
Persistence Probabilities and Exponents.
Series Title: Lecture notes in mathematics (Springer-Verlag), 2149.; Lévy matters, 5.
Other Titles: Lévy matters V
Lévy matters 5
Responsibility: Lars Nørvang Andersen, Søren Asmussen, Frank Aurzada, Peter W. Glynn, Makoto Maejima, Mats Pihlsgård, Thomas Simon.
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Abstract:

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 á 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.

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