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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1101.3038","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-01-16T01:47:55Z","cross_cats_sorted":[],"title_canon_sha256":"5b7610b081fee6a23b133cb2de0fbb00ea6f92c6a1202f0aeb55b458cb6fdaf3","abstract_canon_sha256":"2007999c0324b720d73fd08b168ff210e15bb471c9a30e999b3ddd1fef856caf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:46.488986Z","signature_b64":"YHGDMvMuQNSJ5CiW3x25+KjMMyXyxTMIPCeJKUxYi50kU6vWlTFeSmFAkxakEcS7n5J3ycsoH5QQMDw9+XOvCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d01fef1d2c1b226258d7e79165cea97ecea966e759c02be18136df3699a6e290","last_reissued_at":"2026-05-18T03:38:46.487972Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:46.487972Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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