  Many stochastic time series can be described by a Langevin equation composed
of a deterministic and a stochastic dynamical part. Such a stochastic process
can be reconstructed by means of a recently introduced nonparametric method,
thus increasing the predictability, i.e. knowledge of the macroscopic drift and
the microscopic diffusion functions. If the measurement of a stochastic process
is affected by additional strong measurement noise, the reconstruction process
cannot be applied. Here, we present a method for the reconstruction of
stochastic processes in the presence of strong measurement noise, based on a
suitably parametrized ansatz. At the core of the process is the minimization of
the functional distance between terms containing the conditional moments taken
from measurement data, and the corresponding ansatz functions. It is shown that
a minimization of the distance by means of a simulated annealing procedure
yields better results than a previously used Levenberg-Marquardt algorithm,
which permits a rapid and reliable reconstruction of the stochastic process.
