Before revision:  The existing strong existence and uniqueness results rely on a Lipschitz condition that the intensity of a hybrid marked point process may fail to satisfy. This motivates us to propose a natural pathwise construction that instead requires only sublinear behaviour of the intensity. Using a domination argument, we are able to verify that this construction yields indeed a solution. As we restrict ourselves to non-explosive marked point processes , we also manage to prove uniqueness without any specific assumptionson the intensity .
After revision:  The existing strong existence and uniqueness results rely on a Lipschitz condition that the intensity of a hybrid marked point processes under very general assumptions, extending the results of Massouli\'e (1998) on interacting point processes .