First Passage and First Exit Times for diffusion processes related to a general growth curve

Recently a general growth curve including the well known growth equations, such as Malthus, logistic, Bertallanfy, Gompertz, has been studied. We now propose two stochas- tic formulations of this growth equation. They are obtained starting from a suitable parametrization of the deterministic model, by adding an additive and multiplicative noise respectively. For these processes we focus attention on the First Passage Time from a barrier and on the First Exit Time from a region delimited by two barriers. We consider thresholds, generally time dependent, for which there exist closed-forms of the probability densities of the first passage time and of the first exit time.