  The complex Langevin method aims at performing path integral with a complex
action numerically based on complexification of the original real dynamical
variables. One of the poorly understood issues concerns occasional failure in
the presence of logarithmic singularities in the action, which appear, for
instance, from the fermion determinant in finite density QCD. We point out that
the failure should be attributed to the breakdown of the relation between the
complex weight that satisfies the Fokker-Planck equation and the probability
distribution associated with the stochastic process. In fact, this problem can
occur in general when the stochastic process involves a singular drift term. We
show, however, in a simple example that there exists a parameter region in
which the method works although the standard reweighting method is hardly
applicable.
