By Zhen-Qing Chen
This e-book supplies a entire and self-contained advent to the speculation of symmetric Markov techniques and symmetric quasi-regular Dirichlet varieties. In an in depth and obtainable demeanour, Zhen-Qing Chen and Masatoshi Fukushima hide the fundamental components and purposes of the idea of symmetric Markov techniques, together with recurrence/transience standards, probabilistic capability conception, additive practical idea, and time switch concept. The authors boost the speculation in a basic framework of symmetric quasi-regular Dirichlet types in a unified demeanour with that of standard Dirichlet types, emphasizing the function of prolonged Dirichlet areas and the wealthy interaction among the probabilistic and analytic facets of the idea. Chen and Fukushima then handle the newest advances within the thought, provided right here for the 1st time in any ebook. subject matters comprise the characterization of time-changed Markov approaches by way of Douglas integrals and a scientific account of mirrored Dirichlet areas, and the real roles such advances play within the boundary conception of symmetric Markov processes.
This quantity is a perfect source for researchers and practitioners, and will additionally function a textbook for complicated graduate scholars. It comprises examples, appendixes, and workouts with solutions.