Spectral representations of infinitely divisible processes

Summary The spectral representations for arbitrary discrete parameter infinitely divisible processes as well as for (centered) continuous parameter infinitely divisible processes, which are separable in probability, are obtained. The main tools used for the proofs are (i) a polar-factorization of an arbitrary Lévy measure on a separable Hilbert space, and (ii) the Wiener-type stochastic integrals of non-random functions relative to arbitrary infinitely divisible noise.The research of both authors was supported partially by the AFSOR Grant No. 87-0136; the second named author was also supported partially by a grant from the University of Tennessee