  We consider analytically as well as numerically the finite-size scaling
behavior in the stationary state near the non-equilibrium phase transition of
directed percolation within the mean field regime, i.e., above the upper
critical dimension. Analogous to equilibrium, usual finite-size scaling is
valid below the upper critical dimension, whereas it fails above. Performing a
momentum analysis of associated path integrals we derive modified finite-size
scaling forms of the order parameter and its higher moments. The results are
confirmed by numerical simulations of corresponding high-dimensional lattice
models.
