  Logistic growth models are recurrent in biology, epidemiology, market models,
and neural and social networks. They find important applications in many other
fields including laser modelling. In numerous realistic cases the growth rate
undergoes stochastic fluctuations and we consider a growth model with a
stochastic growth rate modelled via an asymmetric Markovian dichotomic noise.
We find an exact analytical solution for the probability distribution providing
a powerful tool with applications ranging from biology to astrophysics and
laser physics.
