ABSTRACT Accurately forecasting how innovations are adopted is crucial for launching new products and long‐term performance. While traditional diffusion models like the Bass model have been widely used to study adoption trends, they often assume deterministic behavior and overlook the randomness inherent in real‐world markets. Stochastic differential equation (SDE)‐based models offer a more flexible framework by incorporating random fluctuations, typically through additive noise. However, these models rarely account for multiplicative noise, where the intensity of uncertainty increases with the number of adopters. To address this gap, we propose two SDE‐based innovation diffusion models that explicitly include multiplicative noise and consider constant and logistic time‐dependent adoption rates. These models are evaluated using real‐world sales data for technological products, and their performance is compared using established metrics. By incorporating multiplicative uncertainty, the proposed models offer a more realistic representation of adoption dynamics, making them valuable tools for understanding diffusion in uncertain and rapidly evolving markets.
Gaur et al. (Fri,) studied this question.