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Levy matters V = functionals of Levy processes /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Levy matters V/ by Lars Norvang Andersen ... [et al.].
Reminder of title:	functionals of Levy processes /
remainder title:	Levy matters 5
other author:	Andersen, Lars Norvang.
Published:	Cham :Imprint: Springer, : 2015.,
Description:	xvi, 224 p. :ill. (some col.), digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Probability Theory and Stochastic Processes. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-23138-9
ISBN:	9783319231389

Levy matters V = functionals of Levy processes /
Levy matters Vfunctionals of Levy processes /[electronic resource] :Levy matters 5by Lars Norvang Andersen ... [et al.]. - Cham :Imprint: Springer,2015. - xvi, 224 p. :ill. (some col.), digital ;24 cm. - Lecture notes in mathematics,21490075-8434 ;. - Lecture notes in mathematics ;1943..

Makoto Maejima: Classes of infinitely divisible distributions and examples -- Lars Norvang Andersen, Soren Asmussen, Peter W. Glynn and Mats Pihlsgard: Levy processes with two-sided reflection -- Persistence probabilities and exponents -- Frank Aurzada and Thomas Simon: Persistence probabilities and exponents.

This three-chapter volume concerns the distributions of certain functionals of Levy processes. The first chapter, by Makoto Maejima, surveys representations of the main sub-classes of infinitesimal distributions in terms of mappings of certain Levy processes via stochastic integration. The second chapter, by Lars Norvang Andersen, Soren Asmussen, Peter W. Glynn and Mats Pihlsgard, concerns Levy processes reflected at two barriers, where reflection is formulated a 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 Levy process

ISBN: 9783319231389

Standard No.: 10.1007/978-3-319-23138-9doiSubjects--Topical Terms:

593945
Probability Theory and Stochastic Processes.

LC Class. No.: QA274.73

Dewey Class. No.: 519.282

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520 $a This three-chapter volume concerns the distributions of certain functionals of Levy processes. The first chapter, by Makoto Maejima, surveys representations of the main sub-classes of infinitesimal distributions in terms of mappings of certain Levy processes via stochastic integration. The second chapter, by Lars Norvang Andersen, Soren Asmussen, Peter W. Glynn and Mats Pihlsgard, concerns Levy processes reflected at two barriers, where reflection is formulated a 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 Levy process
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