On the development of adoption of newer successive technologies using stochastic differential equation

Abstract

In the literature some models have been proposed to describe the diffusion behavior of the successive generational products based on deterministic new product diffusion models for single generational products. The deterministic models ignore the environmental as well as internal system disturbances. These disturbances create randomness in the adoption process which is likely to be larger in case of generational products. A few single generation diffusion models describe this randomness by introducing stochasticity using Ito's type stochastic differential equations. In this paper, we formulate a mathematical model, that simultaneously describe the adoption pattern of a base technology and substitution effect over the generations of the base product for durable technology product, using stochastic differential equations with continuous state space. The validity of the proposed model is illustrated using four generation IBM Main frame computer data reported in literature.