具有记忆的粒子系统混沌传播的定量估计及其长时间行为
Quantitative propagation of chaos for particle systems with memory and their long-time behaviour
浏览论文内容
中文总结 AI 辅助
本文用耦合方法研究具有记忆的相互作用扩散粒子系统，建立了定量混沌传播估计，并证明在适当条件下大粒子极限与长时间极限可交换。
中文摘要 AI 辅助
我们研究一类具有记忆的相互作用扩散粒子系统及其平均场极限，采用耦合方法。首先，我们为此类模型建立了混沌传播的定量估计。我们的第一个主要结果是在适当的收缩条件下，得到一致时间混沌传播估计。我们还讨论了平稳解存在的条件，并表明向非平稳测度的长时间收敛也可能成立。这需要记忆相互作用的渐近行为和记忆丧失条件。因此，我们的第二个主要结果是粒子系统渐近收敛到相同的平衡态，误差不超过混沌传播误差，这表明大粒子极限和长时间极限是可交换的。
英文摘要
We study a class of interacting diffusion particle systems with memory and their mean-field limit using coupling methods. We first establish quantitative propagation of chaos estimates for this class of models. Our first main result is a uniform-in-time propagation of chaos estimate, under a suitable contraction condition. We also discuss conditions for existence of stationary solutions and show that long-time convergence to a non-stationary measure may also hold. This requires an asymptotic behaviour for the memory interaction and a memory loss condition. As a consequence, our second main result is that the particle system converges asymptotically to the same equilibrium up to the propagation of chaos error, which shows that the large-particle limit and the large-time limit are exchangeable.
