In this paper, we derive elementary M- and optimally robust asymptotic linear (AL)-estimates for the parameters of an Ornstein–Uhlenbeck process. Simulation and estimation of the process are already well-studied, see Iacus (Simulation and inference for stochastic differential equations. Springer, New York, <CitationRef CitationID="CR11">2008</CitationRef>). However, in order to protect against outliers and deviations from the ideal law the formulation of suitable neighborhood models and a corresponding robustification of the estimators are necessary. As a measure of robustness, we consider the maximum asymptotic mean square error (maxasyMSE), which is determined by the influence curve (IC) of AL estimates. The IC represents the standardized influence of an individual observation on the estimator given the past. In a first step, we extend the method of M-estimation from Huber (Robust statistics. Wiley, New York, <CitationRef CitationID="CR10">1981</CitationRef>). In a second step, we apply the general theory based on local asymptotic normality, AL estimates, and shrinking neighborhoods due to Kohl et al. (Stat Methods Appl 19:333–354, <CitationRef CitationID="CR13">2010</CitationRef>), Rieder (Robust asymptotic statistics. Springer, New York, <CitationRef CitationID="CR22">1994</CitationRef>), Rieder (<CitationRef CitationID="CR23">2003</CitationRef>), and Staab (<CitationRef CitationID="CR27">1984</CitationRef>). This leads to optimally robust ICs whose graph exhibits surprising behavior. In the end, we discuss the estimator construction, i.e. the problem of constructing an estimator from the family of optimal ICs. Therefore we carry out in our context the One-Step construction dating back to LeCam (Asymptotic methods in statistical decision theory. Springer, New York, <CitationRef CitationID="CR14">1969</CitationRef>) and compare it by means of simulations with MLE and M-estimator. Copyright Springer-Verlag 2012
