Generalized Feynman–Kac Semigroups, Associated Quadratic Forms and Asymptotic Properties

Abstract

In this paper, we study the Feynman–Kac semigroup T t f(x)=E x[f(X t)exp(N t)], where X t is a symmetric Levy process and N t is a continuous additive functional of zero energy which is not necessarily of bounded variation. We identify the corresponding quadratic form and obtain large time asymptotics of the semigroup. The Dirichlet form theory plays an important role in the whole paper.