In this article, a stochastic innovation diffusion model is proposed, derived from the original logistic growth model assuming that the future remaining growth of the underlying process is not known with certainty but is modeled using an appropriate stochastic process. At any time, the potential adopters of a product are affected by a number of socioeconomic factors that determine their nonuniform behavior, and the way they act is considered to be random. The stochastic model is solved analytically using the theory of reducible stochastic differential equations. The parameter estimators of the model are derived using two procedures for discrete observations of the process. Finally, the model is applied to the data of electricity consumption in Greece and the United States. The prediction of the consumption process is made possible by defining a subdomain such that all possible trajectories of the process should belong within a predefined probability.