{"paper":{"title":"H\\\"{o}lder regularity for operator scaling stable random fields","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"C\\'eline Lacaux (IECN), Hermine Bierm\\'e (MAP5)","submitted_at":"2007-02-02T13:18:13Z","abstract_excerpt":"We investigate the sample paths regularity of operator scaling alpha-stable random fields. Such fields were introduced as anisotropic generalizations of self-similar fields and satisfy a scaling property for a real matrix E. In the case of harmonizable operator scaling random fields, the sample paths are locally H\\\"{o}lderian and their H\\\"{o}lder regularity is characterized by the eigen decomposition with respect to E. In particular, the directional H\\\"{o}lder regularity may vary and is given by the eigenvalues of E. In the case of moving average operator scaling random alpha-stable random fie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0702050","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}