Densities for infinitely divisible random processes

Let {[xi]j(t), t [set membership, variant] [0, T]} J = 1, 2 be infinitely divisible processes with distinct Poisson components and no Gaussian components. Let X be the set of all real-valued functions on [0, T] which are not identically zero, and be the [sigma]-ring generated by the cylinder sets of [xi]j(t), J = 1, 2. Let [mu]j be the measure on induced by [xi]j(t). Necessary and sufficient conditions on the projective limits of the Lévy-Khinchine spectral measures of the processes are found to make [mu]2 << [mu]1, and a representation for the density d[mu]2/d[mu]1 is obtained.