  The behavior of the one-dimensional random-force-driven Burgers equation is
investigated in the path integral formalism on 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-equation) 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.
