  We present several approaches for deriving the coarse-grained continuous
Langevin equation (or Edwards-Wilkinson equation) from a random deposition with
surface relaxation (RDSR) model. First we introduce a novel procedure to divide
the first transition moment into the three fundamental processes involved:
deposition, diffusion and volume conservation. We show how the diffusion
process is related to antisymmetric contribution and the volume conservation
process is related to symmetric contribution, which renormalizes to zero in the
coarse-grained limit. In another approach, we find the coefficients of the
continuous Langevin equation, by regularizing the discrete Langevin equation.
Finally, in a third approach, we derive these coefficients from the set of test
functions supported by the stationary probability density function (SPDF) of
the discrete model. The applicability of the used approaches to other discrete
random deposition models with instantaneous relaxation to a neighboring site is
discussed.
