  This paper deals with the question of conditional sampling and prediction for
the class of stationary max-stable processes which allow for a mixed moving
maxima representation. We develop an exact procedure for conditional sampling
using the Poisson point process structure of such processes. For explicit
calculations we restrict ourselves to the one-dimensional case and use a finite
number of shape functions satisfying some regularity conditions. For more
general shape functions approximation techniques are presented. Our algorithm
is applied to the Smith process and the Brown-Resnick process. Finally, we
compare our computational results to other approaches. Here, the algorithm for
Gaussian processes with transformed marginals turns out to be surprisingly
competitive.
