02855nam a2200397 i 4500991002947969707536160721t20152015sz a b 000 0 eng d978331923137210.1007/978-3-319-23138-9doib14258675-39ule_instBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematicaeng519.223AMS 60-06AMS 60E07AMS 60F99AMS 60G51AMS 60K25LC QA274.73Lévy matters V :functionals of Lévy processes /by Lars Nørvang Andersen ... [et al.]Lévy matters 5Cham [Switzerland] :Springer,2015xvi, 224 p. :ill. (some color.) ;24 cmLecture notes in mathematics,0075-8434 ;2149Includes bibliographical referencesMakoto 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 exponentsThis 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 processLévy processesProbabilitiesAndersen, Lars Nørvangauthorhttp://id.loc.gov/vocabulary/relators/aut739655Lévy matters ;5.b1425867522-11-1621-07-16991002947969707536LE013 60-XX AND21 (2015)12013000293882le013pE46.79-l- 00000.i1578910x22-11-16Lévy matters V1465271UNISALENTOle01321-07-16ma -engsz 00