位移单调线性二次Nash系统的长时间与大群体极限
Long-time and large-population limits of displacement monotone linear-quadratic Nash systems
浏览论文内容
中文总结 AI 辅助
本文针对位移单调线性二次Nash系统，证明均匀时间导数估计，在异质平均场下实现大群体与长时间极限收敛。
中文摘要 AI 辅助
对于具有平均场类缩放和强位移单调数据的线性二次$N$维Nash系统，我们证明了均匀时间先验导数估计，展现出随$N \to \infty$的预期缩放，以便将系统传递到极限。因此，在异质（即非对称）平均场设置中，我们获得了Nash系统在任意长时域$[0,T]$上的均匀时间收敛（当$N \to \infty$时），以及$N$维Nash系统和相应主方程分别向其遍历对应项的收敛（当$T \to \infty$时）。
英文摘要
For linear-quadratic $N$-dimensional Nash systems with mean-field-like scaling and strongly displacement monotone data, we prove uniform-in-time a priori derivative estimates exhibiting the expected scaling as $N \to \infty$ in order to pass the system to the limit. As a consequence, in a heterogeneous (i.e., non-symmetric) mean-field setting, we obtain both uniform-in-time convergence of the Nash system on any arbitrarily long horizon $[0,T]$ (as $N \to \infty$), and convergence of both the $N$-dimensional Nash system and the corresponding master equation to their respective ergodic counterparts (as $T \to \infty$).
发表机构
- University of Rome Tor Vergata（罗马托尔维加塔大学）
机构由 AI 辅助整理，请以论文原文为准。
