  We propose isomorphism type identities for nonlinear functionals of general
infinitely divisible processes. Such identities can be viewed as an analogy of
the Cameron-Martin formula for Poissonian infinitely divisible processes but
with random translations. The applicability of these tools relies on a precise
understanding of L\'evy measures of infinitely divisible processes and their
representations, which are developed here in full generality. We illustrate
this approach on examples of squared Bessel processes, Feller diffusions,
permanental processes, as well as L\'evy processes.
