标题： 一个马尔可夫过程收敛到其平均场极限的简单通用证明 显示英文标题

标题： A simple and general proof for the convergence of Markov processes to their mean-field limits

摘要： 平均场模型通过更简单的微分方程来近似大型随机系统，这些微分方程旨在近似更大系统的均值。通常假设随着随机系统变大（即人数或粒子更多），它们会收敛到平均场模型。平均场模型在许多领域都很常见，但它们的收敛性很少被证明。现有的方法依赖于算子半群、鞅、偏微分方程或无限阶常微分方程组。我们仅使用泰勒定理和基本的常微分方程结果给出了它们收敛的一般证明。我们希望这能使应用研究人员能够常规地证明他们的平均场模型的收敛性，从而使其工作建立在更坚实的基础上。 显示英文摘要

摘要： Mean-field models approximate large stochastic systems by simpler differential equations that are supposed to approximate the mean of the larger system. It is generally assumed that as the stochastic systems get larger (i.e., more people or particles), they converge to the mean-field models. Mean-field models are common in many fields, but their convergence is rarely proved. The existing approaches rely on operator semigroups, martingales, PDEs, or infinite systems of ODEs. We give a general proof for their convergence using only Taylor's theorem and basic ODE results. We hope this allows applied researchers to routinely show convergence of their mean-field models, putting their work on a stronger foundation.