  We present a formalism to derive the stochastic differential equations (SDEs)
for several solid-on-solid growth models. Our formalism begins with a mapping
of the microscopic dynamics of growth models onto the particle systems with
reactions and diffusion. We then write the master equations for these
corresponding particle systems and find the SDEs for the particle densities.
Finally, by connecting the particle densities with the growth heights, we
derive the SDEs for the height variables. Applying this formalism to discrete
growth models, we find the Edwards-Wilkinson equation for the symmetric
body-centered solid-on-solid (BCSOS) model, the Kardar-Parisi-Zhang equation
for the asymmetric BCSOS model and the generalized restricted solid-on-solid
(RSOS) model, and the Villain--Lai--Das Sarma equation for the conserved RSOS
model. In addition to the consistent forms of equations for growth models, we
also obtain the coefficients associated with the SDEs.
