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Symmetric Markov Processes with Tightness Property

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Stochastic Partial Differential Equations and Related Fields (SPDERF 2016)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 229))

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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 \(p_t\).

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The author would like to thank the referee for helpful comments on this paper.

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Correspondence to Masayoshi Takeda .

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Takeda, M. (2018). Symmetric Markov Processes with Tightness Property. In: Eberle, A., Grothaus, M., Hoh, W., Kassmann, M., Stannat, W., Trutnau, G. (eds) Stochastic Partial Differential Equations and Related Fields. SPDERF 2016. Springer Proceedings in Mathematics & Statistics, vol 229. Springer, Cham.

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