  I analyze the Nonlocal Conserved Kardar-Parisi-Zhang (NCKPZ) equation with
spatially correlated noise. This equation is also known as the Nonlocal
Molecular Beam Epitaxy (NMBE) equation andv was originally suggested to study
the effect of the long-range nature of interactions coupled with spatially
correlated noise on the dynamics of a volume conserving surface. I find an
exact result for a subfamily of NCKPZ models in one dimension, and thus
establish an exact result for MBE processes for the first time. Then, to
complete the picture, I construct a Self-Consistent Expansion (SCE) and get
results that are consistent with the exact result in one dimension. I conclude
by discussing previous results obtained for NCKPZ using dynamic renormalization
group approach, and find that this approach does not yield the exact result I
obtain. This discussion shows the advantage of the using SCE to deal with
non-linear stochastic equations.
