Item Details

Print View

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 (Springer-Verlag)
Lévy Matters
ISBN
9783319231372, 3319231375, 9783319231389 (online)
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 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 Two-Sided Reflection
  • Persistence Probabilities and Exponents.
Description
xvi, 224 pages : color illustrations ; 24 cm.
Notes
Includes bibliographical references.
Series Statement
Lecture notes in mathematics, 0075-8434 ; 2149
Lecture notes in mathematics (Springer-Verlag) ; 2149
Lévy matters ; 5
Technical Details
  • Access in Virgo Classic
  • Staff View

    LEADER 02815cam a2200445Mi 4500
    001 u6661978
    003 SIRSI
    005 20151222103302.0
    008 151127s2015 sz a b 000 0 eng d
    020
      
      
    a| 9783319231372 q| (paperback)
    020
      
      
    a| 3319231375 q| (paperback)
    020
      
      
    z| 9783319231389 (online)
    035
      
      
    a| (OCoLC)930610629
    040
      
      
    a| OHX b| eng c| OHX d| ORE
    090
      
      
    a| QA3 .L28 no. 2149
    245
    0
    0
    a| 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.
    264
      
    1
    a| Cham : b| Springer, c| [2015]
    300
      
      
    a| xvi, 224 pages : b| color illustrations ; c| 24 cm.
    336
      
      
    a| text 2| rdacontent
    337
      
      
    a| unmediated 2| rdamedia
    338
      
      
    a| volume 2| rdacarrier
    490
    1
      
    a| Lecture notes in mathematics, x| 0075-8434 ; v| 2149
    504
      
      
    a| Includes bibliographical references.
    505
    0
      
    a| Classes of Infinitely Divisible Distributions and Examples -- Lévy Processes with Two-Sided Reflection -- Persistence Probabilities and Exponents.
    520
      
      
    a| 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.
    650
      
    0
    a| Lévy processes.
    700
    1
      
    a| Andersen, Lars Norvang, e| author.
    700
    1
      
    a| Asmussen, Søren, e| author.
    700
    1
      
    a| Aurzada, Frank e| author.
    700
    1
      
    a| Glynn, Peter W., e| author.
    700
    1
      
    a| Maejima, Makoto, e| author.
    700
    1
      
    a| Pihlsgard, Mats, e| author.
    700
    1
      
    a| Simon, Thomas, e| author.
    776
    0
      
    z| 9783319231389 (online)
    776
    0
      
    w| (GyWOH)har150452900
    830
      
    0
    a| Lecture notes in mathematics (Springer-Verlag) ; v| 2149.
    830
      
    0
    a| Lévy matters ; v| 5.
    596
      
      
    a| 8
    999
      
      
    a| QA3 .L28 no.2149 w| LC i| X031742139 l| STACKS m| MATH t| BOOK
▾See more
▴See less

Availability

Google Preview

Google Books Preview
Library Location Map Availability Call Number
Math Stacks N/A Available