Studying dynamic market size-based adoption modeling & product diffusion under stochastic environment

•New diffusion models are presented by introducing stochasticity in the market growth rate.•Models are validated on the historical sales data of Apple iPhone and Samsung Galaxy phones.•Proposed models exhibited better estimation and fitting capability than the benchmark models.•Empirical analysis ascertain the stochastic market growth of technological innovations.•Findings produces essential managerial insights for policymaking. This study examines the problem of stochasticity in predicting the adoption growth pattern of technological innovations. Two different market expansion-based diffusion models are proposed by calibrating uncertainties in the introduction rate of new potential buyers using the Brownian motion process. The developed stochastic differential equation is described as a forecast model and is solved using the Itô integral and Wiener process. The unique contribution of the present research is that it is capable of describing the dynamicity in the potential market of new products. The proposed methodology is implemented on the Samsung Galaxy and Apple iPhone sales data, and a metaheuristic procedure known as a genetic algorithm is applied to estimate the model parameters. The experimental validation shows that the proposed diffusion models have superior estimation and fitting ability as compared to benchmark models. A rolling cross-validation procedure is performed that demonstrates the excellent forecasting capability of the suggested models. Consequently, the findings of the rigorous and extensive empirical analysis have provided supporting evidence of the stochastic increase in the market size for new products. The proposed stochastic diffusion models can find practical application in the variety of industries for predicting the accurate growth rate of the potential market.