Integral representation for space-time excessive functions

Abstract

We study space-time excessive functions with respect to a basic submarkovian semigroup $\mathbb{P}$. It is shown that under some regularity assumptions many space-time excessive functions on a half-space have a Choquet-type integral represention by suitably choosen densities of the adjoint semigroup $\mathbb{P}^*$. If $\mathbb{P}$ is a convolution semigroup which is absolutely continuous with respect to the Haar measure, then all space-time excessive functions admit such an integral representation.