  The stochastic effective theory approach, often called stochastic inflation,
is widely used in cosmology to describe scalar field dynamics during inflation.
The existing formulations are, however, more qualitative than quantitative
because the connection to the underlying quantum field theory (QFT) has not
been properly established. A concrete sign of this is that the QFT parameters
depend on the renormalisation scale, and therefore the relation between the QFT
and stochastic theory must have explicit scale dependence that cancels it. In
this paper we achieve that by determining the parameters of the second-order
stochastic effective theory of light scalar fields in de Sitter to linear order
in the self-coupling constant $\lambda$. This is done by computing equal-time
two-point correlators to one-loop order both in QFT using dimensional
regularisation and the $\overline{\rm MS}$ renormalisation scheme and the
equal-time four-point correlator to leading order in both theories, and
demanding that the results obtained in the two theories agree. With these
parameters, the effective theory is valid when $m\lesssim H$ and $\lambda^2\ll
m^4/H^4$, and therefore it is applicable in cases where neither perturbation
theory nor any previously proposed stochastic effective theories are.
