{
  "abstract": "In this paper, we study the solvability of backward doubly stochastic differential equations (BDSDEs, for short), both with and without reflection, under weak conditions on the generator. First, when the generator $f$ is of general growth in $y$ and linear growth in $z$, we establish the existence, uniqueness, comparison principle, and the existence of maximal solutions. Second, when $f$ is of linear growth in $y$ and quadratic growth in $z$ with bounded terminal value, we prove the existence, uniqueness, and comparison principle. Finally, when $f$ is of general growth in $y$ and quadratic growth in $z$ with bounded terminal value, we prove the existence of maximal solutions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2603.14447",
  "author_total": 3,
  "authors": [
    {
      "name": "Shuxian Gao"
    },
    {
      "name": "Ying Hu"
    },
    {
      "name": "Jiaqiang Wen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/646qz5j2zz40n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2603.14447",
  "fulltext_url": null,
  "id": "646qz5j2zz40n",
  "issns": [],
  "landing_url": "https://hal.science/hal-05751212v1",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-pr"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
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  "openalex": "W7138163756",
  "pdf_url": "https://hal.science/hal-05751212/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/646qz5j2zz40n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:35Z",
      "native_id": "hal-05751212",
      "source": "hal",
      "url": "https://hal.science/hal-05751212v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-pr",
      "subfield": "probability"
    }
  ],
  "title": "Backward doubly stochastic differential equations with or without reflection under weak conditions",
  "title_text": "Backward doubly stochastic differential equations with or without reflection under weak conditions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:35Z",
  "url": "https://research.draconitic.com/paper/646qz5j2zz40n",
  "venue": "HAL",
  "versions": []
}