  We investigate a Verhulst process, which is the special functional of
geometric Brownian motion and has many applications, among others in biology
and in stochastic volatility models. We present an exact form of density of a
one dimensional distribution of Verhulst process. Simple formula for the
density of Verhulst process is obtained in the special case, when the drift of
geometric Brownian motion is equal to -1/2. Some special properties of this
process are discussed, e.g. it turns out that under Girsanov's change of
measure a Verhulst process still remains a Verhulst process but with different
parameters.
