Uniform propagation of chaos for a dollar exchange econophysics model
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Fecha
2024
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Profesor/a Guía
Facultad/escuela
Idioma
en
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Publisher Cambridge University Press
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Licencia CC
Attribution 4.0 International Deed (CC BY 4.0)
Licencia CC
https://creativecommons.org/licenses/by/4.0/
Resumen
We study the poor-biased model for money exchange introduced in Cao & Motsch ((2023) Kinet. Relat. Models 16(5), 764–794.): agents are being randomly picked at a rate proportional to their current wealth, and then the selected agent gives a dollar to another agent picked uniformly at random. Simulations of a stochastic system of finitely many agents as well as a rigorous analysis carried out in Cao & Motsch ((2023) Kinet. Relat. Models 16(5), 764–794.), Lanchier ((2017) J. Stat. Phys. 167(1), 160–172.) suggest that, when both the number of agents and time become large enough, the distribution of money among the agents converges to a Poisson distribution. In this manuscript, we establish a uniform-in-time propagation of chaos result as the number of agents goes to infinity, which justifies the validity of the mean-field deterministic infinite system of ordinary differential equations as an approximation of the underlying stochastic agent-based dynamics. © The Author(s), 2024.
Notas
Indexación: Scopus
Palabras clave
Agent-based Model, Coupling, Econophysics, Uniform Propagation of Chaos, Wasserstein Distance
Citación
European Journal of Applied Mathematics. 2024
DOI
10.1017/S0956792524000184