  Within the framework of stochastic inflationary cosmology we derive
steady-state distributions P_c(V) of domains in comoving coordinates, under the
assumption of slow-rolling and for two specific choices of the coarse-grained
inflaton potential $V(\Phi)$. We model the process as a Starobinsky-like
equation in V-space plus a time-independent source term P_w(V) which carries
(phenomenologically) quantum-mechanical information drawn from either of two
known solutions of the Wheeler-De Witt equation: Hartle-Hawking's and
Vilenkin's wave functions. The presence of the source term leads to the
existence of nontrivial steady-state distributions P^w_c(V). The relative
efficiencies of both mechanisms at different scales are compared for the
proposed potentials.
