Densities for infinitely divisible random processes

AbstractLet {ξj(t), t ∈ [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 B be the σ-ring generated by the cylinder sets of ξj(t), j = 1, 2. Let μj be the measure on B induced by ξj(t).Necessary and sufficient conditions on the projective limits of the Levy-Khinchine spectral measures of the processes are found to make μ2 ⪡ μ1, and a representation for the density dμ2dμ1 is obtained