A population dependent diffusion model with a stochastic extension
Diffusion modeling is rather broad in nature, and is important in the areas of estimation and forecasting. Conventional models do not incorporate parameters that explicitly take into account the size of the population, or, equivalently, the size of the potential market. As a consequence, the models often fail to provide accurate forecasts, especially when the diffusion process is in the take-off stage. Furthermore, since diffusion is not a strictly deterministic process, forecasts should provide a measure of the underlying uncertainty of the process by incorporating a stochastic process into the formulation of the models. The aim of the present work is to fill this gap by proposing an aggregate diffusion model, the ''population'' diffusion model (PDM), which incorporates the potentially varying market size as a function of the corresponding population. This model realization provides more accurate estimations and future forecasts of the diffusion process, especially when compared to the conventional aggregate diffusion models.