  In this report we summarize a few methods for solving the stochastic
differential equations (SDE) and the corresponding Fokker-Planck equations
describing the Gompertz and logistic random dynamics. It is shown that the
solutions of the Gompertz SDE are completely known, while for the logistic
SDE's we provide the solution as an explicit process, but we can not yet write
down its distributions in closed form. Many details of possible ways out of
this maze are listed in the paper and its appendices. We also briefly discuss
the prospects of performing a suitable averaging, or a deterministic limit. The
possibility is also suggested of associating these equations to the stochastic
mechanics of a quantum harmonic oscillator adopted as a tool serviceable also
in the field of stochastic control: in particular we propose to investigate the
equations associated to the quantum stationary states
