Understanding stochastic perturbation theory: toy models and statistical analysis
arXiv:hep-lat/0002018 · doi:10.1016/S0550-3213(00)00180-2
Abstract
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 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(α^{10})).
16 pages, LaTeX, 11 eps figure