Lévy matters V [electronic resource] : functionals of Lévy processes / by Lars Nørvang Andersen, Søren Asmussen, Frank Aurzada, Peter W. Glynn, Makoto Maejima, Mats Pihlsgård, Thomas Simon.

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Lévy matters V [electronic resource] : functionals of Lévy processes / by Lars Nørvang Andersen, Søren Asmussen, Frank Aurzada, Peter W. Glynn, Makoto Maejima, Mats Pihlsgård, Thomas Simon.

9783319231389 electronic book
3319231383 electronic book
9783319231372

Cham : Springer, 2015.

©2015

English

1 online resource (xvi, 224 pages) : illustrations.

10.1007/978-3-319-23138-9 doi

QA274.73

519.2/82
519.2

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.

Includes bibliographical references.

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Lecture notes in mathematics (Springer-Verlag) ; 2149. 0075-8434
Lévy matters ; 5.

Printed edition: 9783319231372

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