Semi-Dirichlet Forms and Markov Processes

This book deals with analytic treatments of Markov processes. Symmetric Dirichlet forms and their associated Markov processes are important and powerful tools in the theory of Markov processes and their applications. The theory is well studied and used in various fields. In this monograph, we intend to generalize the theory to non-symmetric and time dependent semi-Dirichlet forms. By this generalization, we can cover the wide class of Markov processes and analytic theory which do not possess the dual Markov processes. In particular, under the semi-Dirichlet form setting, the stochastic calculus is not well established yet. In this monograph, we intend to give an introduction to such calculus. Furthermore, basic examples different from the symmetric cases are given. The text is written for graduate students, but also researchers.

"The intention of the author is for the book to serve as a self-contained textbook. The results are therefore mostly followed by detailed proofs. [...] This book, the first systematic treatment of lower bounded semi-Dirichlet forms, will be a valuable contribution to the literature and will certainly become a classic reference in the field." Mathematical Reviews

"This new book is a most welcome addition to the existing literature on Dirichlet forms. It is a readily accessible, advanced graduate-level account of analytic and probabilistic potential theory of Hunt processes given by (lower bounded semi-) Dirichlet forms." Zentralblatt für Mathematik