发表机构
Nanjing Audit University; Institute of Applied Physics and Computational Mathematics; National University of Defense Technology（南京审计大学; 应用物理与计算数学研究所; 国防科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究粗糙噪声驱动的非局部时滞格方程，通过Doss-Sussmann变换和步进法建立适定性，证明随机拉回吸引子存在，并给出数值逼近的收敛性。
AI 中文摘要
我们研究了由无限维平稳弱几何粗糙路径驱动的、定义在$\ell^2(\mathbb Z)$上的具有固定时滞的非局部格方程的路径渐近动力学。利用粗糙流Doss-Sussmann变换和步进法，我们在受控路径框架下建立了全局适定性，并构造了一个连续随机动力系统。我们进一步构造了一个有界拉回吸收族，并利用空间局部化的Lyapunov-Krasovskii泛函，结合驱动粗糙路径空间尾部的缝补估计，证明了格尾部一致消失。通过将此格尾部估计与Arzelà-Ascoli紧性论证相结合，我们建立了唯一随机拉回吸引子的存在性。最后，对于时滞兼容的补偿Euler格式和有限维格截断，我们建立了统一的吸收和格尾部估计，这产生了近似随机拉回吸引子的存在性及其联合上半连续性，而无需时间步长与空间截断水平之间的耦合条件。
英文摘要
We investigate the pathwise asymptotic dynamics of a nonlocal lattice equation with fixed delay on $\ell^2(\mathbb Z)$ driven by an infinite-dimensional stationary weakly geometric rough path. Using a rough-flow Doss-Sussmann transformation and the method of steps, we establish global well-posedness in the controlled-path framework and construct a continuous random dynamical system. We further construct a tempered pullback absorbing family and use a spatially localized Lyapunov-Krasovskii functional, together with a sewing estimate for the spatial tails of the driving rough path, to prove that the lattice tails vanish uniformly. The existence of a unique random pullback attractor is then established by combining this lattice-tail estimate with an Arzelà--Ascoli compactness argument. Finally, for the delay-compatible compensated Euler schemes and finite-dimensional lattice truncations, we establish uniform absorbing and lattice-tail estimates, which yield the existence of the approximate random pullback attractors and their joint upper semicontinuity, without a coupling condition between the time step and the spatial truncation level.
