{
  "annotation_id": "2c07ae64-bdc8-4d9e-8b8e-e598953d7073",
  "date_created": "2026-02-17T05:53:07.514000Z",
  "date_modified": "2026-02-17T05:53:07.514000Z",
  "file_hash": "8f957601a152ed68fef2b046ba8a62540097c5eed81db1ac98716aaa965adb91",
  "private": false,
  "record": {
    "abstract": "We introduce Ising-H\\\"usler-Reiss processes, a new class of multivariate L\\\u0027evy processes that allows for sparse modeling of the path-wise conditional independence structure between marginal stable processes with different stability indices. The underlying conditional independence graph is encoded as zeroes in a suitable precision matrix. An Ising-type parametrization of the weights for each orthant of the L\\\u0027evy measure allows for data-driven modeling of asymmetry of the jumps while retaining an arbitrary sparse graph. We develop consistent estimators for the graphical structure and asymmetry parameters, relying on a new uniform small-time approximation for L\\\u0027evy processes. The methodology is illustrated in simulations and a real data application to modeling dependence of stock returns.",
    "arxiv_id": "2601.06264",
    "authors": [
      "Florian Br\u00fcck",
      "Sebastian Engelke",
      "Stanislav Volgushev"
    ],
    "categories": [
      "stat.ME"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Graph structure learning for stable processes",
    "url": "https://arxiv.org/abs/2601.06264",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f8636580-ddfc-4424-965e-314c94384a7d",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}