  The steady state of the Fokker-Planck equation corresponding to a density
dependent one-step process is approximated by a suitable normal distribution.
Starting from the master equations of the process, written in terms of the time
dependent probabilities, $p_k(t)$ of the states $k=0,1,\ldots , N$, their
continuous (in space) version, the Fokker-Planck equation is formulated. This
PDE approximation enables us to create analytic approximation formulas for the
steady state distribution. These formulas are derived based on heuristic
reasoning and then their accuracy is proved to be of order $1/N^{\beta}$ with
some power $\beta <1$.
