  We consider the nonparametric functional estimation of the drift of a
Gaussian process via minimax and Bayes estimators. In this context, we
construct superefficient estimators of Stein type for such drifts using the
Malliavin integration by parts formula and superharmonic functionals on
Gaussian space. Our results are illustrated by numerical simulations and extend
the construction of James--Stein type estimators for Gaussian processes by
Berger and Wolpert [J. Multivariate Anal. 13 (1983) 401--424].
