  We consider a class of stochastic PDEs of Burgers type in spatial dimension
1, driven by space-time white noise. Even though it is well known that these
equations are well posed, it turns out that if one performs a spatial
discretization of the nonlinearity in the "wrong" way, then the sequence of
approximate equations does converge to a limit, but this limit exhibits an
additional correction term. This correction term is proportional to the local
quadratic cross-variation (in space) of the gradient of the conserved quantity
with the solution itself. This can be understood as a consequence of the fact
that for any fixed time, the law of the solution is locally equivalent to
Wiener measure, where space plays the role of time. In this sense, the
correction term is similar to the usual It\^{o}-Stratonovich correction term
that arises when one considers different temporal discretizations of stochastic
ODEs.
