Bogdan / Graczyk / Byczkowski Potential Analysis of Stable Processes and its Extensions

Erscheinungsjahr 2009
ISBN: 978-3-642-02141-1
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 1980, 194 Seiten, eBook

Reihe: Lecture Notes in Mathematics

Stable Lévy processes and related stochastic processes play an important role in stochastic modelling in applied sciences, in particular in financial mathematics. This book is about the potential theory of stable stochastic processes. It also deals with related topics, such as the subordinate Brownian motions (including the relativistic process) and Feynman–Kac semigroups generated by certain Schrödinger operators. The authors focus on classes of stable and related processes that contain the Brownian motion as a special case.This is the first book devoted to the probabilistic potential theory of stable stochastic processes, and, from the analytical point of view, of the fractional Laplacian. The introduction is accessible to non-specialists and provides a general presentation of the fundamental objects of the theory. Besides recent and deep scientific results the book also provides a didactic approach to its topic, as all chapters have been tested on a wide audience, including young mathematicians at a CNRS/HARP Workshop, Angers 2006.The reader will gain insight into the modern theory of stable and related processes and their potential analysis with a theoretical motivation for the study of their fine properties.

Zielgruppe

Research

Autoren/Hrsg.

Bogdan, Krzysztof

Byczkowski, Tomasz

Kulczycki, Tadeusz

Ryznar, Michal

Song, Renming

Vondracek, Zoran

Graczyk, Piotr

Stos, Andrzej

Inhaltsverzeichnis

Boundary Potential Theory for Schr#x00F6;dinger Operators Based on Fractional Laplacian.- Nontangential Convergence for #x03B1;-harmonic Functions.- Eigenvalues and Eigenfunctions for Stable Processes.- Potential Theory of Subordinate Brownian Motion.