  A correspondence between fluctuations of conformally invariant quantum fields
and that of classical fields finally reducing to perfect fluid matter content
is shown to exist. Previously a similar correspondence between the stress
tensors was known and well established in the 70's. Using recent results
obtained in semiclassical stochastic gravity regarding exact definition and
significance given to quantum fluctuations of the stress tensor, we obtain this
correspondence, which is fundamental to statistical analysis of systems in
curved spacetime. This is of immense importance, in that the fluctuations of
stress tensor play a similar central role in stochastic gravity, as that of the
stress tensor in classical and semiclassical gravity. A relation between the
semiclassical and classical fluctuations therefore, gives insight to the
mesoscopic phenomena for gravitating systems and would further enhance the
perturbative analysis for cosmological spacetime and astrophysical objects,
which is an expansive area of research. Interestingly we see that the quantum
fluctuations have a correspondence with covaiances of pressure and density of
the gravitating system in the stochastic analysis.
