STATISTICAL ERROR DUE TO FINITE TIME AVERAGING IN COMPUTER EXPERIMENTS

In using a computer experiment to calculate the time correlation function of some dynamical variable, the ensemble average over an equilibrium distribution in phase space often is replaced by a time average over a finite interval T. It is shown here that the statistical uncertainty due to this kind of average is of the order of 1T12. The coefficient of the square root is related to a characteristic relaxation time of the correlation function. If only time averaging is performed, the resulting statistical uncertainty in typical computer experiments may be of the order of 20%. © 1969 The American Physical Society.