Lévy Matters V by Sren Asmussen

Lévy Matters V by Sren Asmussen

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.

S�ren Asmussen obtained his PhD at the University of Copenhagen in 1978, followed by the Danish degree of Dr. scient. in 1982. He held academic positions at the University of Copenhagen before moving to Aalborg University in 1987, where he received one of the prestigious Danish research professorships in 1990. In 1995, he became Professor of Mathematical Statistics at Lund University in Sweden, and then moved to his current position as Professor of Applied Probability at Aarhus University in Denmark in 2003. He received the Marcel F. Neuts Applied Probability Prize in 1999, the INFORMS Outstanding Publication Prizes in Simulation in 2002 and 2008, the John von Neumann Theory Prize in 2010, and the gold medal For Great Contributions in Mathematics from the Sobolev Institute of Mathematics, Russian Academy of Sciences in 2011.