Time dependence of moments of an exactly solvable Verhulst model under   random perturbations
  Explicit expressions for one point moments corresponding to stochastic Verhulst model driven by Markovian coloured dichotomous noise are presented. It is shown that the moments are the given functions of a decreasing exponent. The asymptotic behavior (for large time) of the moments is described by a single decreasing exponent. 
V.M. Loginov