Statistical analysis and applications of the multi-sigmoidal deterministic and stochastic logistic growth

We consider a multi-sigmoidal generalization of the logistic growth model. The deterministic model is provided together with its stochastic counterpart. More in detail, we analyse two different birth-death processes with linear and quadratic rates, respectively. From the latter we derive a more manageable diffusive approximation by means of a suitable scaling. Furthermore, we study two possible strategies to obtain the maximum likelihood estimates of the parameters. To validate the described procedures, we conclude with a simulation study. The first-passage-time problem is also addressed.