The asymptotic behaviors of Hawkes information diffusion processes for a large number of individuals
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The dynamics of opinion is a complex and interesting process, especially for the systems with large number individuals. It is usually hard to describe the evolutionary features of these systems. In this paper, we propose a Mckean-Vlasov type integro differential equation to analyze the multi-individual system analytically, and prove that the model has the ability of representing the scaling limit behavior for the large number individuals system in which the interaction is a multivariate Hawkes process with exponential function weight. We show that the coupling between the model and the initial distribution in the equation captures the influence of Hawkes process, which decribes the mutually- exicting and recurrent nature of individuals. Finally we show that the steady state distribution is a "contraction" of the initial distribution in the linear interaction cases.
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