{
  "abstract": "We study a moving-average process with (not necessarily symmetric) Laplace innovations under the constraint of positivity. In the three nondegenerate parameter regimes $0<θ<1$, $θ>1$, and $θ<0$, we prove convergence of the conditioned finite-dimensional distributions and identify the limit as a Doob $h$-transform. The regimes lead to qualitatively different limiting dynamics: the invariant law is supported on the positive half-line for $0<θ<1$, the conditioned chain is confined to the negative half-line for $θ>1$, and the dynamics are genuinely two-sided and governed by $q$-trigonometric functions for $θ<0$. In each case, the persistence exponent, sharp persistence asymptotics, the defining eigenfunction, and the unique invariant distribution are obtained explicitly.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08794",
  "author_total": 2,
  "authors": [
    {
      "name": "Frank Aurzada"
    },
    {
      "name": "Virginia Worf"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fhn7xf53b33je.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08794",
  "fulltext_url": null,
  "id": "fhn7xf53b33je",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08794",
  "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",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7212023145",
  "pdf_url": "https://arxiv.org/pdf/2609.08794",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fhn7xf53b33je.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:01Z",
      "native_id": "2609.08794",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08794"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "MA(1) processes with Laplace innovations conditioned to stay positive",
  "title_text": "MA(1) processes with Laplace innovations conditioned to stay positive",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:01Z",
  "url": "https://research.draconitic.com/paper/fhn7xf53b33je",
  "venue": "arXiv",
  "versions": []
}