Abstract
In this article, we study the problem of estimation of the drift θ of a Gaussian process We give a class of estimators of James-Stein type whose risk is lower than the risk of the maximum likelihood estimator (MLE) under the balanced loss function. Moreover, in the multidimensional case we give a class of Baranchik-type estimators of the drift of a d-dimensional fractional Brownian motion whose risk is lower than the risk of the MLE under a weighted balanced loss function. Finally, we give a numerical simulations to illustrate our results.