Comparison and Analysis of Diffusion Models

Abstract

A real diffusion process consists of a huge amount of interrelated variables. This complexity can be modelled by diffusion models building a simplified mathematical representation of the main features of the process as a time series of indicators describing the phenomenon in interest. Mathematical models are mostly used for technological forecasting purposes; forecasting is based on the best fit of the empirical data to the model formula and trend extrapolation outside the empirical period. The fit gives numeric values to the parameters of the model. Some of the models include also explanative Jactors-values of parameters describe behavioral properties ofthe process. The paper concentrates on mathematical diffusion models. The variety of models derived from the literature is introduced and analyzed. As an application of mathemat ical approach to the diffusion the diffusion of mobile phones is discussed. The focus of this paper is to point out problems in mathematical analysis and to discuss about alternative approaches.