Lévy Matters V
Functionals of Lévy Processes
Seiten
2015
|
1st ed. 2015
Springer International Publishing (Verlag)
978-3-319-23137-2 (ISBN)
Springer International Publishing (Verlag)
978-3-319-23137-2 (ISBN)
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.
Makoto Maejima: Classes of infinitely divisible distributions and examples.- Lars Nørvang Andersen, Søren Asmussen, Peter W. Glynn and Mats Pihlsgard: Lévy processes with two-sided reflection.- Persistence probabilities and exponents.- Frank Aurzada and Thomas Simon: Persistence probabilities and exponents.
| Erscheint lt. Verlag | 5.11.2015 |
|---|---|
| Reihe/Serie | Lecture Notes in Mathematics |
| Lévy Matters | |
| Zusatzinfo | XVI, 224 p. 8 illus., 7 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik |
| Schlagworte | 60E07,60G18,60G51,60K20,60K35 • First passage problem, • Infinitely divisible distribution, • mathematics and statistics • Probability theory and stochastic processes • Reflected Lévy process, • Selfdecomposable distribution, • Self-similar Lévy process |
| ISBN-10 | 3-319-23137-5 / 3319231375 |
| ISBN-13 | 978-3-319-23137-2 / 9783319231372 |
| Zustand | Neuware |
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