Passage time statistics in a stochastic Verhulst model

Using the stochastic paths perturbation approach analytic individual realizations of a stochastic Verhulst model are introduced. The escape of the unstable state is studied for any kind of noise from these individual realizations. We infer from these paths the statistics of the first passage time distribution invoking the solution of an explicit equation with a random coefficient. A stochastic population Verhulst's dynamics with small perturbations of the Wiener class is explicitly worked out. The method can also be implemented for other type of stochastic perturbations like Poisson-noise (shot white pulses), etc.