Levy Matters I: Recent Progress In Theory And Applications: Foundations, Trees And Numerical Issues In Finance (lecture Notes In Mathematics)
by Thomas Duquesne /
2010 / English / PDF
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Focusing on the breadth of the topic, this volume explores Levy processes and applications, and presents the state-of-the-art in this evolving area of study. These expository articles help to disseminate important theoretical and applied research to those studying the fieldThis is the first volume of a subseries of the Lecture Notes in Mathematics called Levy Matters, which will appear randomly over the next years. Each volume will describe some important topic in the theory or applications of Levy 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 Levy 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 Levy or additive processes model the dynamics of the risky assets.
