Let X = (Ω,ℱ,ℱt,Xt,𝜃t,Px)
be a special standard Markov process with state space (E,g) and transition
semigroup (Pt). We emphasize here that the ℱt are the usual completions of the
natural σ-fields for the process. In this paper, we associate with certain multiplicative
functionals of X operators on the class of excessive functions which are related to the
operators PM but which are a bit unusual in probabilistic potential theory in that
they are not generally determined by kernels on E ×ℰ. An application is given to a
problem treated by P.-A. Meyer concerning natural potentials dominated by an
excessive function.
