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Symmetric Markov Processes, Time Change, and Boundary Theory (LMS-35)$
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Zhen-Qing Chen and Masatoshi Fukushima

Print publication date: 2011

Print ISBN-13: 9780691136059

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691136059.001.0001

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Boundary Theory for Symmetric Markov Processes

Boundary Theory for Symmetric Markov Processes

Chapter:
(p.300) Chapter Seven Boundary Theory for Symmetric Markov Processes
Source:
Symmetric Markov Processes, Time Change, and Boundary Theory (LMS-35)
Author(s):

Zhen-Qing Chen

Masatoshi Fukushima

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691136059.003.0007

This chapter proposes a boundary theory for symmetric Markov processes. It begins by investigating the relationship between the space (Fₑ,E) and the space ((⁰)ref, 0,ref). Next, the chapter focuses on the restricted spaces ₀∣F, F and their descriptions in terms of the Feller measures U, V, and Uα‎ and the Douglas integrals defined by them. The chapter then introduces the lateral condition for the L² generator and studies the case where the set F consists of countably many points that are located in an invariant way under a quasi-homeomorphism. It then turns to one-point extensions and examples of these, and follows up with many-point extensions and their examples as well.

Keywords:   boundary theory, reflected Dirichlet spaces, reflecting extensions, Douglas integrals, lateral condition, countable boundary, one-point extensions, many-point extensions

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