Continuous approximation of a random walk

We consider the problem of nucleation affected by pre-existing nuclei which can be treated as a one-step random process described by a nonlinear master equation (ME). We construct a nontrivial time-dependent expression for the flux of nucleated particles and demonstrate that in the sense of a specific criterion-the time lag of transient nucleation-this expression satisfies the ME with asymptotic accuracy. A Fokker-Planck approximation to the ME which describes correctly both nucleation and growth is also constructed.