Item Details
Lévy Matters V: Functionals of Lévy Processes
Lars Nørvang Andersen, Søren Asmussen, Frank Aurzada, Peter W. Glynn, Makoto Maejima, Mats Pihlsgård, Thomas Simon
 Format
 Book
 Published
 Cham : Springer, [2015]
 Language
 English
 Series
 Lecture Notes in Mathematics
 Lecture Notes in Mathematics (SpringerVerlag)
 Lévy Matters
 ISBN
 9783319231372, 3319231375, 9783319231389 (online)
 Summary
 This threechapter volume concerns the distributions of certain functionals of Lévy processes. The first chapter, by Makoto Maejima, surveys representations of the main subclasses 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.
 Contents
 Classes of Infinitely Divisible Distributions and Examples
 Lévy Processes with TwoSided Reflection
 Persistence Probabilities and Exponents.
 Description
 xvi, 224 pages : color illustrations ; 24 cm.
 Notes
 Includes bibliographical references.
 Series Statement
 Lecture notes in mathematics, 00758434 ; 2149
 Lecture notes in mathematics (SpringerVerlag) ; 2149
 Lévy matters ; 5
 Technical Details

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LEADER 02855cam a2200457Mi 4500001 u6661978003 SIRSI005 20151222103302.0008 151127s2015 sz a b 000 0 eng da 9783319231372 q (paperback)a 3319231375 q (paperback)z 9783319231389 (online)a (Sirsi) o930610629a (OCoLC)930610629a OHX b eng c OHX d OREa QA3 .L28 no. 2149a Lévy Matters V : b functionals of Lévy processes / c Lars Nørvang Andersen, Søren Asmussen, Frank Aurzada, Peter W. Glynn, Makoto Maejima, Mats Pihlsgård, Thomas Simon.a Cham : b Springer, c [2015]a xvi, 224 pages : b color illustrations ; c 24 cm.a text 2 rdacontenta unmediated 2 rdamediaa volume 2 rdacarriera Lecture notes in mathematics, x 00758434 ; v 2149a Includes bibliographical references.a Classes of Infinitely Divisible Distributions and Examples  Lévy Processes with TwoSided Reflection  Persistence Probabilities and Exponents.a This threechapter volume concerns the distributions of certain functionals of Lévy processes. The first chapter, by Makoto Maejima, surveys representations of the main subclasses 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.a Lévy processes.a Andersen, Lars Norvang, e author.a Asmussen, Søren, e author.a Aurzada, Frank e author.a Glynn, Peter W., e author.a Maejima, Makoto, e author.a Pihlsgard, Mats, e author.a Simon, Thomas, e author.z 9783319231389 (online)w (GyWOH)har150452900a Lecture notes in mathematics (SpringerVerlag) ; v 2149.a Lévy matters ; v 5.a 8a QA3 .L28 no.2149 w LC i X031742139 l STACKS m MATH t BOOK
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QA3 .L28 no.2149 