Stochastic origin of Gompertzian growths

Abstract: This work faces the problem of the origin of the logarithmic character of the Gompertzian growth. We show that the macroscopic, deterministic Gompertz equation describes the evolution from the initial state to the final stationary value of the median of a log-normally distributed, stochastic process. Moreover, by exploiting a stochastic variational principle, we account for self-regulating feature of Gompertzian growths provided by self-consistent feedback of relative density variations. This well defined conceptual framework shows its usefulness by allowing a reliable control of the growth by external actions.