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Levy Matters V - Functionals of Levy Processes (Paperback, 1st ed. 2015)
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Levy Matters V - Functionals of Levy Processes (Paperback, 1st ed. 2015)
Series: Lecture Notes in Mathematics, 2149
Expected to ship within 10 - 15 working days
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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.
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