{"paper":{"title":"Heat content for convolution semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Tomasz Grzywny, Wojciech Cygan","submitted_at":"2016-06-29T16:01:08Z","abstract_excerpt":"Let $\\mathbf{X}=\\{X_t\\}_{t\\geq 0}$ be a L\\'evy process in $\\mathbb{R}^d$ and $\\Omega$ be an open subset of $\\mathbb{R}^d$ with finite Lebesgue measure. In this article we consider the quantity $H (t) = \\int_{\\Omega}\\mathbb{P}_{x} (X_t\\in \\Omega ^c) dx$ which is called the heat content. We study its asymptotic behaviour as $t$ goes to zero for isotropic L\\'evy processes under some mild assumptions on the characteristic exponent. We also treat the class of L\\'evy processes with finite variation in full generality."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.09168","kind":"arxiv","version":2},"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"}