A stochastic innovation-diffusion model incorporating dynamic potential market

Abstract

The next best thing to be able to peep into the future is to be able to predict it accurately. With enterprises increasingly relying upon innovation, they wish to predict how their new products and services will be absorbed and accepted in the market. Several mathematical models help in predicting innovation diffusion in the market so that sound decisions on production, quantities and finance could be taken. Continuing that effort to predict innovation diffusion more accurately, we have developed and analyzed a stochastic model of innovation diffusion by depicting a dynamic potential market. Whenever the potential adopter population is substantial and the products considered are durable, the adoption process assumes a stochastic form. Here, we suggest a stochastic innovation-diffusion model assuming the potential market to be dynamic in nature. The stochastic model is solved analytically by applying the stochastic differential equation. The change point concept is also incorporated in the model by assuming that adoption rate of product per remaining potential adopter might change due to shift in marketing strategy. Estimation of parameters in the model is illustrated for applicability and accuracy. Predictive validity and MSE have been employed to examine the effectiveness of the proposed model and the values are compared with other existing models to demonstrate its efficiency.