On a Non-homogeneous Gompertz-Type Diffusion Process: Inference and First Passage Time
A stochastic diffusion model based on a generalized Gompertz deterministic growth in which the carrying capacity depends on the initial size of the population is considered. The growth parameter of the process is then modified by introducing a time-dependent exogenous term. The first passage time problem is considered and a two-step procedure to estimate the model is proposed. Simulation study is also provided for suitable choices of the exogenous term.