Lévy Matters V : Functionals of Lévy Processes

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 ch...

Full description

Main Authors: Andersen, Lars Nørvang, Asmussen, Søren (Author), Aurzada, Frank (Author), Glynn, Peter W. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Cham Springer International Publishing 2015, 2015
Edition:1st ed. 2015
Series:Lévy Matters, A Subseries on Lévy Processes
Subjects:
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
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 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.  
Physical Description:XVI, 224 p. 8 illus., 7 illus. in color online resource
ISBN:9783319231389