Lévy Matters I

Fractional Integrals and Extensions of Selfdecomposability.- Packing and Hausdorff Measures of Stable Trees.- Numerical Analysis of Additive, Lévy and Feller Processes with Applications to Option Pricing.

This is the first volume of a subseries of the Lecture Notes in Mathematics which will appear randomly over the next years. Each volume will describe some important topic in the theory or applications of Lévy processes and pay tribute to the state of the art of this rapidly evolving subject with special emphasis on the non-Brownian world. The three expository articles of this first volume have been chosen to reflect the breadth of the area of Lévy processes. The first article by Ken-iti Sato characterizes extensions of the class of selfdecomposable distributions on R^d. The second article by Thomas Duquesne discusses Hausdorff and packing measures of stable trees. The third article by Oleg Reichmann and Christoph Schwab presents numerical solutions to Kolmogoroff equations, which arise for instance in financial engineering, when Lévy or additive processes model the dynamics of the risky assets.

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 Includes supplementary material: sn.pub/extras