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© 2009

Potential Analysis of Stable Processes and its Extensions

  • Piotr Graczyk
  • Andrzej Stos
Book

Part of the Lecture Notes in Mathematics book series (LNM, volume 1980)

Also part of the Ecole d'Eté Probabilit.Saint-Flour book sub series (volume 1980)

Table of contents

  1. Front Matter
    Pages 1-8
  2. Piotr Graczyk, Andrzej Stos
    Pages 1-24
  3. R. Song, Z. Vondraček
    Pages 87-176
  4. Back Matter
    Pages 1-16

About this book

Introduction

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 Schroedinger 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.

Keywords

Brownian motion Lévy process Stochastic processes alpha-harmonic functions fractional Laplacian probabilistic potential theory stable processes stochastic process subordinate processes

Authors and affiliations

  1. 1.Inst. Mathematics & Computer ScienceWroclaw University of TechnologyWroclawPoland
  2. 2.Inst. Mathematics & Computer ScienceWroclaw University of TechnologyWroclawPoland
  3. 3.Inst. MathematicsPAN WroclawWroclawPoland
  4. 4.Inst. Mathematics & Computer ScienceWroclaw University of TechnologyWroclawPoland
  5. 5.Dept. MathematicsUniversity of Illinois, UrbanaUrbanaU.S.A.
  6. 6.Dept. MathematicsUniversity of ZagrebZagrebCroatia

Editors and affiliations

  • Piotr Graczyk
    • 1
  • Andrzej Stos
    • 2
  1. 1.Labo. Angevin de Recherche enUniversitè AngersAngers CX 01France
  2. 2.Labo. MathématiquesUniversité Clermont-Ferrand IIAubière CXFrance

Bibliographic information

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Reviews

From the reviews:

“The book is a collection of articles on all aspects of the potential theory of stable processes on Rd, written by well-known experts in this field, thereby summarizing recent results in various papers in a unified presentation. … readers interested in the subject will find this book extremely helpful.” (Wilhelm Stannat, Mathematical Reviews, Issue 2011 i)

“Recently, a lot of progress has been made in the potential theory of stable processes and related Lévy processes. This book is a collection of surveys on some of these recent results made into a book form. This book should be very useful for researchers and graduate students to read the recent progress in the potential theory of stable processes and their generalizations.” (Renming Song, Zentralblatt MATH, Vol. 1203, 2011)