Tohoku Mathematical Journal
2016
June
SECOND SERIES VOL. 68, NO. 2

Tohoku Math. J.
68 (2016), 161-197

Title LARGE DEVIATION PRINCIPLES FOR GENERALIZED FEYNMAN-KAC FUNCTIONALS AND ITS APPLICATIONS

Author Daehong Kim, Kazuhiro Kuwae and Yoshihiro Tawara

(Received August 4, 2014, revised September 19, 2014)
Abstract. Large deviation principles of occupation distribution for generalized Feyn-man-Kac functionals are presented in the framework of symmetric Markov processes having doubly Feller or strong Feller property. As a consequence, we obtain the $L^p$-independence of spectral radius of our generalized Feynman-Kac functionals. We also prove Fukushima's decomposition in the strict sense for functions locally in the domain of Dirichlet form having energy measure of Dynkin class without assuming no inside killing.

Mathematics Subject Classification. Primary 31C25; Secondary 35B50, 60J45, 35J, 53C, 58.
Key words and phrases. Large deivation principle, Feynman-Kac semigroup, symmetric Markov processes, Dirichlet forms, occupation distribution, spectral bound, additive functional, continuous additive functional of zero energy, Kato class, local Kato class, extended Kato class, Feller property, strong Feller property, doubly Feller property.

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