  The behaviour of the one--dimensional random--forced Burgers equation is
investigated in the path integral formalism, using a discrete space--time
lattice. We show that by means of Monte Carlo methods one may evaluate
observables, such as structure functions, as ensemble averages over different
field realizations. The regularization of shock solutions to the
zero--viscosity limit (Hopf-eq.) eventually leads to constraints on lattice
parameters, required for the stability of the simulations. Insight into the
formation of localized structures (shocks) and their dynamics is obtained.
