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

For Markov processes in weak duality, we study time changes, decompositions of Revuz measure, and potentials of additive functionals which may charge [zeta], 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.Markov processes time change additive functionals Revuz measure entrance law Ray-Knight compactification Riesz decomposition h-path transform