{
  "annotation_id": "13989023-9dbf-4beb-9ff6-cec4d1562807",
  "date_created": "2026-02-17T05:53:07.568000Z",
  "date_modified": "2026-02-17T05:53:07.568000Z",
  "file_hash": "44e50a06045b8e5258dc5dca6a877579c608222ebeb6e27c91926e00d6c4a13a",
  "private": false,
  "record": {
    "abstract": "We study the existence and uniqueness of rank-based interacting systems of stochastic differential equations. These systems can be seen as modifications with state-dependent coefficients of the Atlas model in mathematical finance. The coefficients of the underlying SDEs are possibly discontinuous. We first establish strong well-posedness for a planar system with rank-dependent drift coefficients, and non-rank-dependent and non-uniformly elliptic diffusion coefficients. We then state weak well-posedness for two classes of high-dimensional rank-based interacting SDEs with elliptic diffusion coefficients. Finally, we address the positivity of solutions in the case where the diffusion coefficients vanish at zero.",
    "arxiv_id": "2601.06383",
    "authors": [
      "H\u00e9l\u00e8ne Gu\u00e9rin",
      "Nathalie Krell"
    ],
    "categories": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Well-posedness of state-dependent rank-based interacting systems",
    "url": "https://arxiv.org/abs/2601.06383",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5f6a1ebe-bc73-4d9d-a806-c9536c533bc1",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}