Mathematics – Probability
Scientific paper
2010-03-25
Mathematics
Probability
13 pages, to appear in SIAM Journal on Applied Mathematics
Scientific paper
We study a general stochastic rumour model in which an ignorant individual has a certain probability of becoming a stifler immediately upon hearing the rumour. We refer to this special kind of stifler as an uninterested individual. Our model also includes distinct rates for meetings between two spreaders in which both become stiflers or only one does, so that particular cases are the classical Daley-Kendall and Maki-Thompson models. We prove a Law of Large Numbers and a Central Limit Theorem for the proportions of those who ultimately remain ignorant and those who have heard the rumour but become uninterested in it.
Lebensztayn Elcio
Machado Fábio P.
Rodriguez Pilar Montañés
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