Stationarity and uniform in time convergence for the graphon particle system

Erhan Bayraktar and Ruoyu Wu

Stochastic Processes and their Applications, 2022, vol. 150, issue C, 532-568

Abstract: We consider the long time behavior of heterogeneously interacting diffusive particle systems and their large population limit. The interaction is of mean field type with weights characterized by an underlying graphon. The limit is given by a graphon particle system consisting of independent but heterogeneous nonlinear diffusions whose probability distributions are fully coupled. Under suitable assumptions, including a certain convexity condition, we show the exponential ergodicity for both systems, establish the uniform-in-time law of large numbers for marginal distributions as the number of particles increases, and introduce the uniform-in-time Euler approximation. The precise rate of convergence of the Euler approximation is provided.

Keywords: Graphon particle systems; Heterogeneous interaction; Exponential ergodicity; Long time behavior; Uniform in time law of large numbers; Uniform in time Euler approximations (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2022.04.006

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