  In the present paper we provide the closed form of the path-like solutions
for the logistic and $\theta$-logistic stochastic differential equations, along
with the exact expressions of both their probability density functions and
their moments. We simulate in addition a few typical sample trajectories, and
we provide a few examples of numerical computation of the said closed formulas
at different noise intensities: this shows in particular that an increasing
randomness - while making the process more unpredictable - asymptotically tends
to suppress in average the logistic growth. These main results are preceded by
a discussion of the noiseless, deterministic versions of these models: a
prologue which turns out to be instrumental - on the basis of a few simplified
but functional hypotheses - to frame the logistic and $\theta$-logistic
equations in a unified context, within which also the Gompertz model emerges
from an anomalous scaling.
