  Based on the central limit theorem, we discuss the problem of evaluation of
the statistical error of Monte Carlo calculations using a time discretized
diffusion process. We present a robust and practical method to determine the
effective variance of general observables and show how to verify the
equilibrium hypothesis by the Kolmogorov-Smirnov test. We then derive scaling
laws of the efficiency illustrated by Variational Monte Carlo calculations on
the two dimensional electron gas.
