Functionals of Lévy processes
Author(s)
Bibliographic Information
Functionals of Lévy processes
（Lecture notes in mathematics, 2149 . Lévy matters ; 5）
Springer, c2015
- Other Title
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Lévy Matters : a subseries on Lévy processes
Lévy Matters V
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
L/N||LNM||2149200033897913
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Note
Other authors: Søren Asmussen, Frank Aurzada, Peter W. Glynn, Makoto Maejima, Mats Pihlsgård, Thomas Simon
"Bernoulli Society for Mathematical Statistics and Probability"--Cover
"The volumes in this subseries are published under the auspices of the Bernoulli Society"--p. [ii]
Includes bibliographical references
Description and Table of Contents
Description
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.
Table of Contents
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.
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