{"paper":{"title":"Harnack Inequalities for Ornstein-Uhlenbeck Processes Driven by L\\'{e}vy Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jian Wang","submitted_at":"2011-05-15T18:19:04Z","abstract_excerpt":"By using the existing sharp estimates of density function for rotationally invariant symmetric $\\alpha$-stable L\\'{e}vy processes and rotationally invariant symmetric truncated $\\alpha$-stable L\\'{e}vy processes, we obtain that Harnack inequalities hold for rotationally invariant symmetric $\\alpha$-stable L\\'{e}vy processes with $\\alpha\\in(0,2)$ and Ornstein-Uhlenbeck processes driven by rotationally invariant symmetric $\\alpha$-stable L\\'{e}vy process, while logarithmic Harnack inequalities are satisfied for rotationally invariant symmetric truncated $\\alpha$-stable L\\'{e}vy processes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2958","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"}