The asymptotic behaviors of self excitation information diffusion processes for a large number of individuals

TL;DR

This paper analyzes the long-term behavior of a self-excitation opinion model for large populations, showing it converges to a distribution described by a McKean-Vlasov equation, with steady states being contractions of initial opinions.

Contribution

It introduces a McKean-Vlasov integro-differential equation framework for large-scale self-excitation opinion dynamics, extending understanding of asymptotic behaviors.

Findings

Asymptotic behaviors described by a McKean-Vlasov equation.

Steady state distributions are contractions of initial distributions in linear cases.

Model captures mutual excitation and recurrent nature of opinions.

Abstract

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 study the self excitation opinion model, which has been shown the superior performance in learning and predicting opinions. We study the asymptotic behaviors of this model for large number of individuals, and prove that the asymptotic behaviors of the model in which the interaction is a multivariate self excitation process with exponential function weight, can be described by a Mckean-Vlasov type integro differential equation. The coupling between this equation and the initial distribution captures the influence of self excitation 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.