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Symmetric Markov Processes, Time Change, and Boundary Theory (LMS-35) by Zhenqing Chen, Masatoshi Fukushima

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Chapter Seven

 

BOUNDARY THEORY FOR SYMMETRIC MARKOV PROCESSES

Let X0 be an m0-symmetric right process on a state space E0. The boundary theory of symmetric Markov processes concerns all possible symmetric extensions of X0 to some state space image containing E0 as an intrinsic open subset so that they admit no-sojourn (that is, spend zero Lebesgue amount of time) at image \ E0. The no-sojorn condition ensures that the extension process is m0-symmetric after the measure m0 is extended to by setting m0( \ E0) = 0. The initial “minimal” process X0 can be taken ...

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