Tohoku Mathematical Journal

Large deviation principles for generalized Feynman-Kac functionals and its applications

Daehong Kim, Kazuhiro Kuwae, and Yoshihiro Tawara

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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.

Article information

Source
Tohoku Math. J. (2), Volume 68, Number 2 (2016), 161-197.

Dates
First available in Project Euclid: 17 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1466172769

Digital Object Identifier
doi:10.2748/tmj/1466172769

Mathematical Reviews number (MathSciNet)
MR3514698

Zentralblatt MATH identifier
1348.31005

Subjects
Primary: 31C25: Dirichlet spaces
Secondary: 35B50: Maximum principles 60J45: Probabilistic potential theory [See also 31Cxx, 31D05] 35J 53C 58

Keywords
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

Citation

Kim, Daehong; Kuwae, Kazuhiro; Tawara, Yoshihiro. Large deviation principles for generalized Feynman-Kac functionals and its applications. Tohoku Math. J. (2) 68 (2016), no. 2, 161--197. doi:10.2748/tmj/1466172769. https://projecteuclid.org/euclid.tmj/1466172769


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