We construct Nicolai maps for N = 2 supersymmetric extensions of minis
uperspace models. It is shown that Nicolai maps exist for only a very
restricted set of states. In the models considered these are the two s
tates corresponding to the empty and the filled fermion sectors. The f
orm of the Nicolai maps in these sectors is given explicitly, and it i
s shown that they have a natural stochastic interpretation. This resul
t also suggests a probabilistic interpretation of the wave function.