{"paper":{"title":"A note on the generalized heat content for L\\'evy processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Tomasz Grzywny, Wojciech Cygan","submitted_at":"2017-03-31T08:23:17Z","abstract_excerpt":"Let $\\mathbf{X}=\\{X_t\\}_{t\\geq 0}$ be a L\\'{e}vy process in $\\mathbb{R}^d$ and $\\Omega$ be an open subset of $\\mathbb{R}^d$ with finite Lebesgue measure. The quantity $H (t) = \\int_{\\Omega} \\mathbb{P}^{x} (X_t\\in \\Omega ^c) d x$ is called the heat content. In this article we consider its generalized version $H_g^\\mu (t) = \\int_{\\mathbb{R}^d}\\mathbb{E}^{x} g(X_t)\\mu( d x )$, where $g$ is a bounded function and $\\mu$ a finite Borel measure. We study its asymptotic behaviour at zero for various classes of L\\'{e}vy processes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10790","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"}