Modelos de difusão de inovação em grafos

• Ano de defesa: 2019
• Autor(a) principal: Oliveira, Karina Bindandi Emboaba de
• Orientador(a): Rodriguez, Pablo Martin
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de São Carlos; Câmpus São Carlos
• Programa de Pós-Graduação: Programa Interinstitucional de Pós-Graduação em Estatística - PIPGEs
• Palavras-chave em Português: Difusão de inovação; Cadeias de Markov dependentes da densidade; Processo de contato; Teoremas limites; Modelos com "social reinforcement"
• Palavras-chave em Inglês: Innovation diffusion; Density dependent Markov chains; Contact process; Limit theorems; Social reinforcement models
• Área do conhecimento CNPq: CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA
• Link de acesso: https://repositorio.ufscar.br/handle/20.500.14289/11535

Areas such as politics, economics and marketing are heavily influential in terms of information diffusion. For this reason, several branches of science have studied such phenomena in order to simulate and understand them by mathematical and/or stochastic models. In this context, this phd project aims to generalize innovation diffusion models that there is in the literature. The first model uses the social reinforcement mechanism for diffusion of innovation and which was built for the complete graph. In this case, we consider a finite population, closed, totally mixed and subdivided into four classes of individuals called ignorants, aware, adopters and abandoner of innovation. We prove a Law of Large Numbers and a Central Limit Theorem for the proportion of the population who have never heard about the innovation and those who know about ir but they have not adopted it yet. In addition, we also obtain result for the convergence of the maximum of adopter in a stochastic interval, as well as the instant of time that the process reaches that state. For this study, we used results of the theory of density dependent Markov chains. Furthermore, we formulated a stochastic model with structure stages to describe the phenomenon of innovation diffusion in a structured population. More precisely, we proposed a continuous time Markov chain defined in a population represented by the d-dimensional integer lattice. Each individual of the population must be in some of the M + 1 states belonging to the set {0,1,2,...,M}. In this sense, 0 stands for ignorant, i for i in {1,...,M-1} for aware in stage i and M for adopter. The arguments, that allow to obtain sufficient conditions under which the innovation either becomes extinct or survives with positive probability, are studied.