{"paper":{"title":"Hunt's hypothesis (H) and Getoor's conjecture for L\\'{e}vy Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Wei Sun, Ze-Chun Hu","submitted_at":"2011-01-16T01:47:55Z","abstract_excerpt":"In this paper, Hunt's hypothesis (H) and Getoor's conjecture for L\\'{e}vy processes are revisited. Let $X$ be a L\\'{e}vy process on $\\mathbf{R}^n$ with L\\'{e}vy-Khintchine exponent $(a,A,\\mu)$. {First, we show that if $A$ is non-degenerate then $X$ satisfies (H). Second, under the assumption that $\\mu({\\mathbf{R}^n\\backslash \\sqrt{A}\\mathbf{R}^n})<\\infty$, we show that $X$ satisfies (H) if and only if the equation $$ \\sqrt{A}y=-a-\\int_{\\{x\\in {\\mathbf{R}^n\\backslash \\sqrt{A}\\mathbf{R}^n}:\\,|x|<1\\}}x\\mu(dx),\\ y\\in \\mathbf{R}^n, $$ has at least one solution. Finally, we show that if $X$ is a sub"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3038","kind":"arxiv","version":3},"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"}