TY - BOOK ID - 8211300 TI - Potential analysis of stable processes and its extensions AU - Bogdan, Krzysztof AU - Stos, Andrzej AU - Graczyk, P. AU - SpringerLink (Online service) PY - 2009 SN - 3642021409 9786612655791 1282655795 3642021417 PB - Berlin, Germany : Springer, DB - UniCat KW - Functional analysis. KW - Potential theory (Mathematics). KW - Stochastic process. KW - Potential theory (Mathematics) KW - Functional analysis KW - Civil & Environmental Engineering KW - Mathematics KW - Mathematical Statistics KW - Operations Research KW - Engineering & Applied Sciences KW - Physical Sciences & Mathematics KW - Green's operators KW - Green's theorem KW - Potential functions (Mathematics) KW - Potential, Theory of KW - Functional calculus KW - Mathematics. KW - Mathematical models. KW - Probabilities. KW - Probability Theory and Stochastic Processes. KW - Mathematical Modeling and Industrial Mathematics. KW - Potential Theory. KW - Probability KW - Statistical inference KW - Combinations KW - Chance KW - Least squares KW - Mathematical statistics KW - Risk KW - Models, Mathematical KW - Simulation methods KW - Mathematical analysis KW - Mechanics KW - Math KW - Science KW - Calculus of variations KW - Functional equations KW - Integral equations KW - Distribution (Probability theory. KW - Distribution functions KW - Frequency distribution KW - Characteristic functions KW - Probabilities KW - Analyse fonctionnelle. UR - https://www.unicat.be/uniCat?func=search&query=sysid:8211300 AB - 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. ER -