Levy Matters V: Functionals Of Levy Processes
by Lars Norvang Andersen /
2013 / English / PDF
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This three-chapter volume concerns the distributions of certain functionals of Lvy processes. The first chapter, by Makoto Maejima, surveys representations of the main sub-classes of infinitesimal distributions in terms of mappings of certain Lvy processes via stochastic integration. The second chapter, by Lars Nrvang Andersen, Sren Asmussen, Peter W. Glynn and Mats Pihlsgrd, concerns Lvy processes reflected at two barriers, where reflection is formulated 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 Lvy process.
