A STOCHASTIC GENERALIZATION OF THE BASS DIFFUSION-MODEL

A stochastic version of the Bass model is developed to account for uncertainty inherent in the innovation diffusion process. Solution to the stochastic differential equation is obtained using two different approaches: (a) the perturbation expansion method, and (b) the operator method. The properties of the mean and variance functions of the diffusion model are analyzed. The derived analytical results provide additional insights into the nature of the diffusion process. These results have important implications for statistical estimation and inference, marketing-mix planning and new product forecasting.