Symmetric Markov processes and large deviation theory

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The integrability of Feynman-Kac functional is called gaugeability or conditional gaugeability. The conditional gaugeability is closely related to the subcriticality of Schrodinger operators, that is, the existence of the Green function. In this study, we obtained a necessary and sufficient condition for conditional gaugeability; moreover we showed the equivalence between conditional gaugeability and subcriticality of generalized Schrodinger operators. We applied this condition to show the subcriticality of concrete Schrodinger operators; for example, we considered the Schrodinger operator whose potential is the surface measure of sphare. We obtained a necessary and sufficient condition the Schrodinger operator being subcritical in terms of the radius of the sphere. To prove the necessary and sufficient condition for conditional gaugeability, we extended the full large deviation principle of Donsker-Varadhan type to symmetric Markov processes with finite lifetime and applied it to a time changed process of the Brownian motion.