Modeling and analysis of uncertain Bass diffusion model driven by uncertain Liu process

Bo Li and Ziyu Tao

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 13, 4121-4140

Abstract: The Bass diffusion model is one of the most influential models for predicting the diffusion of new products and technologies, but the diffusion process will be affected by some uncertain factors. Usually, such kinds of uncertain factors are characterized as stochastic processes. However, in many cases, this approach can lead to uncertain issues. Therefore, in this article, a Bass diffusion model that incorporates the uncertainty theory is studied. First, we present an uncertain Bass diffusion model where the uncertain disturbance is modeled as an uncertain Liu process. Then, the existence and uniqueness of the uncertain Bass diffusion model are analyzed. Moreover, the uncertain Bass diffusion model is solved by using the 99-α-Runge-Kutta method. Finally, we carry out a numerical simulation on the output of the integrated circuit industry in China by using uncertain differential equations and stochastic differential equations. The results show that modeling with uncertain differential equations is superior to using stochastic differential equations.

Date: 2025
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DOI: 10.1080/03610926.2024.2413848

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