Homogeneous random measures for Markov processes in weak duality: Study via an entrance boundary

AbstractFor Markov processes in weak duality, we study time changes, decompositions of Revuz measure, and potentials of additive functionals which may charge ζ, the lifetime of the process. The basic tools are a Ray-Knight (entrance) compactification, Dynkin's;theory of minimal excessive measures, and a process with random birth and death. In the last section, we work out an example of our techniques, involving entrance laws for one-dimensional diffusions