Understanding stochastic perturbation theory: toy models and statistical analysis Original Research Article

The numerical stochastic perturbation method based on Parisi–Wu quantisation is applied to a suite of simple models to test its validity at high orders. Large deviations from normal distribution for the basic estimators are systematically found in all cases (“Pepe effect”). As a consequence one should be very careful in estimating statistical errors. We present some results obtained on Weingartenʹs “pathological” model where reliable results can be obtained by an application of the bootstrap method. We also present some evidence that in the far less trivial application to lattice gauge theory a similar problem should not arise at moderately high loops (up to O(α10) ).