  We develop a method for treating a series of secularly growing terms obtained
from quantum perturbative calculations: autonomous first-order differential
equations are constructed such that they reproduce this series to the given
order. The exact solutions of these equations are free of secular terms and
approach a finite limit at late times. This technique is illustrated for the
well-known problem of secular growth of correlation functions of a massless
scalar field with a quartic self-interaction in de Sitter space. For the
expectation value of the product of two fields at coinciding space-time points
we obtain a finite late-time result that is very close to the one following
from Starobinsky's stochastic approach.
