Capacities of Symmetric Markov Processes

1988 ◽  
pp. 159-170
Author(s):  
J. Glover ◽  
W. Hansen ◽  
M. Rao
Keyword(s):  
Markov Processes ◽  
Symmetric Markov Processes

Flux and Lateral Conditions for Symmetric Markov Processes

2008 ◽  
Vol 29 (3) ◽  
pp. 241-269
Author(s):  
Zhen-Qing Chen ◽  
Masatoshi Fukushima
Keyword(s):  
Markov Processes ◽  
Symmetric Markov Processes

Boundary Theory for Symmetric Markov Processes

2011 ◽  
Author(s):  
Zhen-Qing Chen ◽  
Masatoshi Fukushima
Keyword(s):  
Markov Processes ◽  
Boundary Theory ◽  
Symmetric Markov Processes ◽  
The Relationship ◽  
Lateral Condition

This chapter proposes a boundary theory for symmetric Markov processes. It begins by investigating the relationship between the space (Fₑ,E) and the space ((ℱ⁰)ref, ℰ 0,ref). Next, the chapter focuses on the restricted spaces ℱ₀∣F, ℱ∣F and their descriptions in terms of the Feller measures U, V, and U α‎ 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.

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