{
  "abstract": "In this work, we are concerned with a class of multi-dimensional time-inhomogeneous stochastic differential equations (SDEs) on $\\R^d$ driven by pure-jump Lévy processes, where the drift coefficient $b(t,x)$ satisfies $\\lim_{t\\to \\infty}b(t,x) =0$ for every $x\\in \\R^d$. On account of three regimes associated with the index $α$ of large jumps corresponding to the driven Lévy noise, we investigate the quantitative asymptotics of the corresponding rescaled processes. More precisely, for $α\\in (0,2)$, we prove that the rescaled processes, governed by time-inhomogeneous SDEs subject to additive processes, converge with respect to suitably chosen Wasserstein distances to time-homogeneous SDEs driven by symmetric $α$-stable processes. Notably, the driven noise in the limiting SDEs depends only on large jumps of the underlying additive processes. In case of $α\\ge2$, a phase transition occurs and a diffusive phenomenon arises. In particular, in the setting $α>2$, we establish the ergodicity of the rescaled process by means of asymptotic pseudotrajectories. The resulting time-homogeneous limiting SDEs are driven by Brownian motions, even though the transformed time-inhomogeneous SDEs are driven by (discontinuous) additive processes, and the effective noise intensity is determined by the entire Lévy measure of the original pure-jump process. As far as the critical case $α=2 $ is concerned, we demonstrate that the noise intensity of the limiting SDEs driven by Brownian motions relies merely on the large-jump part of the Lévy measure.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11657",
  "author_total": 2,
  "authors": [
    {
      "name": "Jianhai Bao"
    },
    {
      "name": "Jian Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cpeest4ss9nzb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11657",
  "fulltext_url": null,
  "id": "cpeest4ss9nzb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11657",
  "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.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7212245318",
  "pdf_url": "https://arxiv.org/pdf/2609.11657",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cpeest4ss9nzb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11657",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11657"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Quantitative Asymptotics for Time-Inhomogeneous Lévy-Driven SDEs with Asymptotically Vanishing Drifts",
  "title_text": "Quantitative Asymptotics for Time-Inhomogeneous Lévy-Driven SDEs with Asymptotically Vanishing Drifts",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/cpeest4ss9nzb",
  "venue": "arXiv",
  "versions": []
}