Limit theorems for a stochastic model of adoption and abandonment innovation on homogeneously mixing populations

Autor(es)

Oliveira, K. B. E. ^[1] ; Rodriguez, P. M. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, ICMC, Sao Carlos - Brazil

^[2] Univ Fed Pernambuco, UFPE, Recife, PE - Brazil

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT; v. 2020, n. 3 MAR 2020.
• Citações Web of Science: 0

Resumo

In this work we study a modified stochastic version of the well known Bass model of innovation diffusion. In the considered model, an innovation spreads through an homogeneously mixing population which is subdivided into four classes of individuals, namely, ignorants, aware, adopters and abandoners. These classes are related to the participation level of each individual in the spreading procedure. An individual in ignorant or aware state becomes an adopter due to the influence of other adopters in the population. On the other hand, any adopter can spontaneously abandon the innovation, thus becoming an abandoner, at constant rate. We measure the impact of the innovation spreading by studying the remaining proportion of population who have never heard about the innovation and those who know about it but they have not adopted it yet. This is accomplished by proving a law of large numbers and a central limit theorem. In addition, we discuss the behavior of the maximum of adopters during the process, as well as the instant of time in which the process reaches this quantity. (AU)

• Processo FAPESP: 16/11648-0 - Teoremas limite e resultados de transição de fase para modelos de propagação de informação em grafos
• Beneficiário: Pablo Martin Rodriguez
• Linha de fomento: Auxílio à Pesquisa - Regular
• Processo FAPESP: 17/10555-0 - Modelagem estocástica de sistemas interagentes
• Beneficiário: Fabio Prates Machado
• Linha de fomento: Auxílio à Pesquisa - Temático