  I describe a recently derived stochastic approach to inflaton dynamics which
can address some serious problems associated with conventional inflationary
theory. Using this theory I derive an exact solution to the stochastic dynamics
for the case of a $\lambda\phi^4$ potential and use it to study the generated
primordial density fluctuations. It is found that on both sub and super-horizon
scales the theory predicts gaussian fluctuations to a very high accuracy along
with a near scale-invariant spectrum. Of most interest is that the amplitude
constraint is found to be satisfied for $\lambda\sim 10^{-5}$ rather than
$\lambda\sim 10^{-14}$ of the conventional theory. This represents a dramatic
easing of the fine-tuning constraints, a feature likely to generalize to a wide
range of potentials.
