  We consider the one-dimensional KPP-equation driven by space-time white
noise. We show that for all parameters above the critical value for survival,
there exist stochastic wavelike solutions which travel with a deterministic
positive linear speed. We further give a sufficient condition on the initial
condition of a solution to attain this speed. Our approach is in the spirit of
corresponding results for the nearest-neighbor contact process respectively
oriented percolation. Here, the main difficulty arises from the moderate size
of the parameter and the long range interaction. Stopping times and averaging
techniques are used to overcome this difficulty.
