Markov processes with creation of mass-redefinition and decomposition theorem

AbstractThe paper redefines Markov processes with a random starting time (MPCA) in a more general way so as to remove an aesthetic defect of the former definition. The process {Xt, Ft: t⩾0} was formally defined on a σ-finite measure space (Ω, F, Px) (x in the state space) but the dependence of Px upon x did not have a probabilistic meaning. Also the former construction used a creation measure φx in which the dependence of φx upon x is even less meaningful. The reason x appeared in the definition was because of applications to perturbation theory of Markov process. The new definition and existence proof give a wider class of MPCA. The processes obtained in perturbation theory constitute only a subclass of it.A decomposition of MPCA into Markov processes in the usual sense, according to a “starting time measure,” is also given