Conditional propagation of chaos in a spatial stochastic epidemic model with common noise

2021/11/04 by Vuong, Yen V., Hauray, Maxime, Pardoux, Etienne · 2 citations
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2111.02733

Abstract

We study a stochastic spatial epidemic model where the N individuals carry two features: a position and an infection state, interact and move in \R^d. In this Markovian model, the evolution of the infection states are described with the help of the Poisson Point Processes , whereas the displacement of the individuals are driven by mean field advection, a (state dependence) diffusion and also a common noise, so that the spatial dynamic is a random process. We prove that when the number N of individual goes to infinity, the conditional propagation of chaos holds : conditionnally to the common noise, the individuals are asymptotically independent and the stochastic dynamic converges to a "random" nonlinear McKean-Vlasov process. As a consequence, the associated empirical measure converges to a measure, which is solution of a stochastic mean-field PDE driven by the common noise.

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