{"paper":{"title":"On weak uniqueness and distributional properties of a solution to an SDE with $\\alpha$-stable noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexei Kulik","submitted_at":"2015-10-31T09:44:54Z","abstract_excerpt":"For an SDE driven by a rotationally invariant $\\alpha$-stable noise we prove weak uniqueness of the solution under the balance condition $\\alpha+\\gamma>1$, where $\\gamma$ denotes the Holder index of the drift coefficient. We prove existence and continuity of the transition probability density of the corresponding Markov process and give a representation of this density with an explicitly given \"principal part\", and a \"residual part\" which possesses an upper bound. Similar representation is also provided for the derivative of the transition probability density w.r.t. the time variable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00106","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"}