On divergence of expectations of the Feynman–Kac type with singular potentials

Abstract

Motivated by the work of Baras–Goldstein (1984), we discuss when expectations of the Feynman–Kac type with singular potentials are divergent. Underlying processes are Brownian motion and $\alpha$-stable process. In connection with the work of Ishige–Ishiwata (2012) concerned with the heat equation in the half-space with a singular potential on the boundary, we also discuss the same problem in the half-space for the case of Brownian motion.