{
  "abstract": "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07076",
  "author_total": 3,
  "authors": [
    {
      "name": "Lijuan Zhang"
    },
    {
      "name": "Jiangwei Zhang"
    },
    {
      "name": "Jianhua Huang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/41eyd9d7n23s8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07076",
  "fulltext_url": null,
  "id": "41eyd9d7n23s8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07076",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2207|Stability and Controllability of Differential Equations"
    ]
  ],
  "openalex": "W7220937936",
  "pdf_url": "https://arxiv.org/pdf/2610.07076",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/41eyd9d7n23s8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.07076",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07076"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Random Pullback Attractors and Numerical Approximation for Nonlocal Lattice Delay Equations Driven by Rough Noise",
  "title_text": "Random Pullback Attractors and Numerical Approximation for Nonlocal Lattice Delay Equations Driven by Rough Noise",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/41eyd9d7n23s8",
  "venue": "arXiv",
  "versions": []
}