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

Stein estimation for the drift of Gaussian processes using the Malliavin calculus