A new Gompertz-type diffusion process with application to random growth.

Stochastic models describing growth kinetics are very important for predicting many biological phenomena. In this paper, a new Gompertz-type diffusion process is introduced, by means of which bounded sigmoidal growth patterns can be modeled by time-continuous variables. The main innovation of the process is that the bound can depend on the initial value, a situation that is not provided by the models considered to date.