A Large Deviation Principle for Symmetric Markov Processes with Feynman–Kac Functional

Abstract

We establish a large deviation principle for the occupation distribution of a symmetric Markov process with Feynman–Kac functional. As an application, we show the L p -independence of the spectral bounds of a Feynman–Kac semigroup. In particular, we consider one-dimensional diffusion processes and show that if no boundaries are natural in Feller’s boundary classification, the L p -independence holds, and if one of the boundaries is natural, the L p -independence holds if and only if the L 2-spectral bound is non-positive.