  We examine the effects of introducing a wall or edge into a directed
percolation process. Scaling ansatzes are presented for the density and
survival probability of a cluster in these geometries, and we make the
connection to surface critical phenomena and field theory. The results of
previous numerical work for a wall can thus be interpreted in terms of surface
exponents satisfying scaling relations generalising those for ordinary directed
percolation. New exponents for edge directed percolation are also introduced.
They are calculated in mean-field theory and measured numerically in 2+1
dimensions.
