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.
Rezensionen / Stimmen
From the reviews:
"The book is a collection of articles on all aspects of the potential theory of stable processes on R
d
, 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)
Reihe
Sprache
Verlagsort
Verlagsgruppe
Illustrationen
13 s/w Abbildungen
X, 194 p. 13 illus.
Dateigröße
ISBN-13
978-3-642-02141-1 (9783642021411)
DOI
10.1007/978-3-642-02141-1
Schweitzer Klassifikation
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.
