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

An exact analytical solution for generalized growth models driven by a Markovian dichotomic noise