  This article is devoted to the numerical study of various finite difference
approximations to the stochastic Burgers equation. Of particular interest in
the one-dimensional case is the situation where the driving noise is white both
in space and in time. We demonstrate that in this case, different finite
difference schemes converge to different limiting processes as the mesh size
tends to zero. A theoretical explanation of this phenomenon is given and we
formulate a number of conjectures for more general classes of equations,
supported by numerical evidence.
