$L^p$-independence of growth bounds of Feynman–Kac semigroups

Abstract

The theory of Dirichlet forms is an $L^2$-theory, while the theory of Markov processes is, in a sense, an $L^1$-theory. To bridge this gap, we study the $L^p$-independence of growth bounds of Markov semigroups, more generally, of generalized Feynman–Kac (Schrödinger) semigroups. A key idea for the proof of the $L^p$-independence is to employ arguments in the Donsker-Varadhan large deviation theory.