Additive functionals of several Levy processes and intersection local times

Different extensions of an isomorphism theorem of Dynkin are developed and are used to study two distinct but related families of functionals of Levy processes; n-fold "near-intersections" of a single Levy process and continu ous additive functionals of several independent Levy processes. Intersectio n local times for n independent Levy processes are also studied. They are r elated to both of the above families. In all three cases sufficient conditi ons are obtained for the almost sure continuity of these functionals in ter ms of the almost sure continuity of associated Gaussian chaos processes. Co ncrete sufficient conditions are given for the almost sure continuity of th ese functionals of Levy processes.