Understanding stochastic perturbation theory: toy models and statistical analysis

The numerical stochastic perturbation method based on Parisi-Wu quantisatio n is applied to a suite of simple models to test its validity at high order s. Large deviations from normal distribution for the basic estimators are s ystematically found in all cases ("Pepe effect"). As a consequence one shou ld be very careful in estimating statistical errors. We present some result s obtained on Weingarten's "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(alpha( 10))). (C) 2000 Elsevier Science B.V. All rights reserved.