This book gives a comprehensive and self-contained introduction to the theory of symmetric Markov processes and symmetric quasi-regular Dirichlet forms. In a detailed and accessible manner, Zhen-Qing Chen and Masatoshi Fukushima cover the essential elements and applications of the theory of symmetric Markov processes, including recurrence/transience criteria, probabilistic potential theory, additive functional theory, and time change theory. The authors develop the theory in a general framework of symmetric quasi-regular Dirichlet forms in a unified manner with that of regular Dirichlet forms, emphasizing the role of extended Dirichlet spaces and the rich interplay between the probabilistic and analytic aspects of the theory. Chen and Fukushima then address the latest advances in the theory, presented here for the first time in any book. Topics include the characterization of time-changed Markov processes in terms of Douglas integrals and a systematic account of reflected Dirichlet spaces, and the important roles such advances play in the boundary theory of symmetric Markov processes.
This volume is an ideal resource for researchers and practitioners, and can also serve as a textbook for advanced graduate students. It includes examples, appendixes, and exercises with solutions.
"This book is an extremely valuable contribution to the literature on symmetric Markov processes and Dirichlet forms and will certainly become a classic reference in the field."--Zoran Vondracek, Mathematical Reviews
"This monograph is written very carefully. In summary, it is an ideal resource for researchers and very advanced graduate students in the field of Dirichlet forms and Hunt processes."--Michael Voit, Zentralblatt MATH
"The presentation is comprehensive and self contained though it requires solid previous knowledge on theoretic probability together with some notions on measure theory and functional analysis. The volume can serve as textbook for graduate students or as a reference for researchers on the field."--Marco Castrillon Lopez, European Mathematical Society
"This is an excellent book that provides a systematic treatment of one of the most fundamental concepts in modern probability theory. It will certainly find lots of interest among all mathematicians who work at the interplay of stochastics and analysis."--Karl-Theodor Sturm, University of Bonn
"Modern theory of Dirichlet forms is widely considered to be one of the main achievements in the analysis of stochastic process, and the authors of this book are among the world's leading experts in the field."--Michael Röckner, Bielefeld University