On representations of stochastic processes by Radon measures on D(0,1)

We provide a necessary and sufficient condition for a stochastic process X = {Xt : t ∈ [0, 1]}, taking values in a real Banach space B, for the existence of a probability Radon measure on the space D((0, 1), B) such that the process {et : t ∈ [0, 1]} consisting of evaluationfunctionals is distributed as X. The condition may be easy verified for Levy processes.