{
  "abstract": "We study a two-dimensional degenerate stochastic differential equation with oblique reflection and spectrally positive strictly stable noise of index in $(1,2)$, motivated by join-the-shortest-queue systems with heavy-tailed interarrival times. A polynomial-exponential Lyapunov function and fixed-time minorization establish positive Harris recurrence and exponential ergodicity in weighted total variation. We construct the invariant law from a stable path and prove its absolute continuity. Regulator identities describe stationary dependence and recover the joint Laplace transform from the queue marginal. Idleness inherits the classical stable Ornstein-Uhlenbeck tail; the queue has a sharp exponential tail with a polynomial prefactor whose power is half the stable index and a positive constant represented through regeneration. Conditional on small idleness, idleness divided by the conditioning threshold and the queue converge to independent beta and size-biased limits. Under large-queue conditioning, normalized idleness and queue excess converge to independent Mittag-Leffler and exponential limits.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39471",
  "author_total": 2,
  "authors": [
    {
      "name": "Guodong Pang"
    },
    {
      "name": "Wei You"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2s0e5kfk8kvbk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39471",
  "fulltext_url": null,
  "id": "2s0e5kfk8kvbk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39471",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39471",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2s0e5kfk8kvbk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39471",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39471"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Exponential Ergodicity and Invariant Distribution of a Degenerate Reflected SDE with Stable Noise",
  "title_text": "Exponential Ergodicity and Invariant Distribution of a Degenerate Reflected SDE with Stable Noise",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/2s0e5kfk8kvbk",
  "venue": "arXiv",
  "versions": []
}