  We compute the growth of the mean square of quantum fluctuations of test
fields with small effective mass during a slowly changing, nearly de Sitter
stage which took place in different inflationary models. We consider a
minimally coupled scalar with a small mass, a modulus with an effective mass $
\propto H^2$ (with $H$ as the Hubble parameter) and a massless non-minimally
coupled scalar in the test field approximation and compare the growth of their
relative mean square with the one of gauge-invariant inflaton fluctuations. We
find that in most of the single field inflationary models the mean square gauge
invariant inflaton fluctuation grows {\em faster} than any test field with a
non-negative effective mass. Hybrid inflationary models can be an exception:
the mean square of a test field can dominate over the gauge invariant inflaton
fluctuation one on suitably choosing parameters. We also compute the stochastic
growth of quantum fluctuation of a second field, relaxing the assumption of its
zero homogeneous value, in a generic inflationary model; as a main result, we
obtain that the equation of motion of a gauge invariant variable associated,
order by order, with a generic quantum scalar fluctuation during inflation can
be obtained only if we use the number of e-folds as the time variable in the
corresponding Langevin and Fokker-Planck equations for the stochastic approach.
We employ this approach to derive some bounds in the case of a model with two
massive fields.
