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.
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