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.
