In this paper a stochastic innovation diffusion model is proposed derived by introducing stochasticity into the well-known Bass model. The stochastic model is solved analytically by using the theory of reducible stochastic differential equations and the first moment of the resulting stochastic process is presented. The parameter estimators of the model are derived by using a procedure which provides the maximum likelihood estimators (MLE) using time series data. Finally, the model is applied to the data of electricity consumption in Greece. Using a simulation technique, it is possible to predict the performance of the consumption process by defining a subdomain to which all possible trajectories of the process should belong with a predefined probability.