Shakshi Singhal
Department of Operational Research, University of Delhi, Delhi-110007, India.

Adarsh Anand
Department of Operational Research, University of Delhi, Delhi-110007, India.

Ompal Singh
Department of Operational Research, University of Delhi, Delhi-110007, India.

DOI https://dx.doi.org/10.33889/IJMEMS.2019.4.3-055

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Abstract

Diffusion models are rigorously implemented in marketing research to predict the actual trend of innovations over time. These models can be classified in terms of deterministic and stochastic behavior. Deterministic models ignore the randomness in the adoption rate of an innovation that occurs due to environmental and internal system disturbances. Therefore, in the present research, a generalized stochastic diffusion model using Itô’s process is proposed that jointly study the product awareness and eventual adoption of an innovation. Convolution function is applied to integrate these two processes. In addition, different probability distributions are employed, which are relevant for describing the product awareness and adoption processes. Non-linear regression is further carried out to validate the proposed models and parameters are estimated based on the actual sales data from Smartphone and automobile industries. The forecasting results indicate that the proposed models perform empirically better than the already established diffusion models.

Keywords- Awareness, Convolution, Itô’s integral, Stochastic differential equation, Technology diffusion.

Citation

Singhal, S., Anand, A., & Singh, O. (2019). SDE based Generalized Innovation Diffusion Modeling. International Journal of Mathematical, Engineering and Management Sciences, 4(3), 697-707. https://dx.doi.org/10.33889/IJMEMS.2019.4.3-055.