Cohen, S., Kuznetsov, A., Kyprianou, A.E., Rivero, V.
2013, XII, 186 p. 8 illus., 1 illus. in color.
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Over the past 10-15 years, we have seen a revival of general Lévy processes theory as well as a burst of new applications
There is a lively and growing research community in this area
Expository articles help to disseminate important theoretical and applied research to other researchers and in particular to young researchers like PhD students and Postdocs
Chapters attract different focus groups of readers
This is the second volume in a subseries of the Lecture Notes in Mathematics called Lévy Matters, which is published at irregular intervals over the years. Each volume examines a number of key topics in the theory or applications of Lévy processes and pays tribute to the state of the art of this rapidly evolving subject with special emphasis on the non-Brownian world.
The expository articles in this second volume cover two important topics in the area of Lévy processes. The first article by Serge Cohen reviews the most important findings on fractional Lévy fields to date in a self-contained piece, offering a theoretical introduction as well as possible applications and simulation techniques. The second article, by Alexey Kuznetsov, Andreas E. Kyprianou, and Victor Rivero, presents an up to date account of the theory and application of scale functions for spectrally negative Lévy processes, including an extensive numerical overview.
Content Level »Research
Keywords »60G10, 60G40, 60G51, 60G70, 60J10, 60J45 - excursion theory for Lévy processes - fluctuation theory for subordinators - fractional Lévy field - scale functions for subordinators