  We analyze the Gaussian approximation as a method to obtain the first and
second moments of a stochastic process described by a master equation. We
justify the use of this approximation with ideas coming from van Kampen's
expansion approach (the fact that the probability distribution is Gaussian at
first order). We analyze the scaling of the error with a large parameter of the
system and compare it with van Kampen's method. Our theoretical analysis and
the study of several examples shows that the Gaussian approximation turns out
to be more accurate. This could be specially important for problems involving
stochastic processes in systems with a small number of particles.
