  A large class of quantum and statistical field theoretical models,
encompassing relevant condensed matter and non-abelian gauge systems, are
defined in terms of complex actions. As the ordinary Monte-Carlo methods are
useless in dealing with these models, alternative computational strategies have
been proposed along the years. The Langevin technique, in particular, is known
to be frequently plagued with difficulties such as strong numerical
instabilities or subtle ergodic behavior. Regarding the chirally decomposed
version of the sine-Gordon model as a prototypical case for the failure of the
Langevin approach, we devise a truncation prescription in the stochastic
differential equations which yields numerical stability and is assumed not to
spoil the Berezinskii-Kosterlitz-Thouless transition. This conjecture is
supported by a finite size scaling analysis, whereby a massive phase ending at
a line of critical points is clearly observed for the truncated stochastic
model.
