  We propose a way how to generate a max-stable process in $C[0,1]$ from a
max-stable random vector in $\mathbb R^d$ by generalizing the \emph{max-linear
model} established by \citet{wansto11}. It turns out that if the random vector
follows some finite dimensional distribution of some initial max-stable
process, the approximating processes converge uniformly to the original process
and the pointwise mean squared error can be represented in a closed form. The
obtained results carry over to the case of generalized Pareto processes. The
introduced method enables the reconstruction of the initial process only from a
finite set of observation points and, thus, reasonable prediction of max-stable
processes in space becomes possible. A possible extension to arbitrary
dimension is outlined.
