Symmetric Markov Processes with Tightness Property
A symmetric Markov process X is said to be in Class (T) if it is irreducible, strong Feller and possesses a tightness property. We give some properties of X in Class (T) and of the semi-group \(p_t\) of X: the uniform large deviation principle of X, \(L^p\)-independence of growth bounds of \(p_t\), compactness of \(p_t\) as an operator in \(L^2\), and boundedness of every eigenfunction of \(p_t\).
KeywordsSymmetric Markov process Dirichlet form Compactness of semigroup
2010 Mathematics Subject Classification60J45 60G52 31C25
The author would like to thank the referee for helpful comments on this paper.
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