{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:N3HMBDRCQBAPJLFMS2LZML4746","short_pith_number":"pith:N3HMBDRC","schema_version":"1.0","canonical_sha256":"6ecec08e228040f4acac9697962f9fe79c8dcefa6221df6899f3853ad66b02d5","source":{"kind":"arxiv","id":"1209.4919","version":4},"attestation_state":"computed","paper":{"title":"On certain integral functionals of squared Bessel processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Umut \\c{C}etin","submitted_at":"2012-09-21T20:58:20Z","abstract_excerpt":"Let $X$ be a squared Bessel process. Following a Feynman-Kac approach, the Laplace transforms of joint laws of $(U, \\int_0^{R_y}X_s^p\\,ds)$ are studied where $R_y$ is the first hitting time of $y$ by $X$ and $U$ is a random variable measurable with respect to the history of $X$ until $R_y$. A subset of these results are then used to solve the associated small ball problems for $\\int_0^{R_y}X_s^p\\,ds$ and determine a Chung's law of iterated logarithm. $(\\int_0^{R_y}X_s^p\\,ds)$ is also considered as a purely discontinuous increasing Markov process and its infinitesimal generator is found. The fi"},"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":"1209.4919","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-09-21T20:58:20Z","cross_cats_sorted":[],"title_canon_sha256":"18e3a97e4b01efa6f89a7a30953ccfbb7e38e211b1c4409e6788231ab27e8056","abstract_canon_sha256":"5fb75cd449a34a716718dd4b4aff1dd90d35fbd4586097f4e7ffb2dd5740855d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:56:00.171799Z","signature_b64":"QERS9t/4VJoUfoL1f7WyK+2Vz9g1XCPOTJkTO9LWgxwLraAlkc0y0vJT9ZAFONOQ4u85CWJnt4akg0eGrk3GAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ecec08e228040f4acac9697962f9fe79c8dcefa6221df6899f3853ad66b02d5","last_reissued_at":"2026-05-18T01:56:00.171304Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:56:00.171304Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On certain integral functionals of squared Bessel processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Umut \\c{C}etin","submitted_at":"2012-09-21T20:58:20Z","abstract_excerpt":"Let $X$ be a squared Bessel process. Following a Feynman-Kac approach, the Laplace transforms of joint laws of $(U, \\int_0^{R_y}X_s^p\\,ds)$ are studied where $R_y$ is the first hitting time of $y$ by $X$ and $U$ is a random variable measurable with respect to the history of $X$ until $R_y$. A subset of these results are then used to solve the associated small ball problems for $\\int_0^{R_y}X_s^p\\,ds$ and determine a Chung's law of iterated logarithm. $(\\int_0^{R_y}X_s^p\\,ds)$ is also considered as a purely discontinuous increasing Markov process and its infinitesimal generator is found. The fi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4919","kind":"arxiv","version":4},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1209.4919","created_at":"2026-05-18T01:56:00.171386+00:00"},{"alias_kind":"arxiv_version","alias_value":"1209.4919v4","created_at":"2026-05-18T01:56:00.171386+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4919","created_at":"2026-05-18T01:56:00.171386+00:00"},{"alias_kind":"pith_short_12","alias_value":"N3HMBDRCQBAP","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"N3HMBDRCQBAPJLFM","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"N3HMBDRC","created_at":"2026-05-18T12:27:16.716162+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/N3HMBDRCQBAPJLFMS2LZML4746","json":"https://pith.science/pith/N3HMBDRCQBAPJLFMS2LZML4746.json","graph_json":"https://pith.science/api/pith-number/N3HMBDRCQBAPJLFMS2LZML4746/graph.json","events_json":"https://pith.science/api/pith-number/N3HMBDRCQBAPJLFMS2LZML4746/events.json","paper":"https://pith.science/paper/N3HMBDRC"},"agent_actions":{"view_html":"https://pith.science/pith/N3HMBDRCQBAPJLFMS2LZML4746","download_json":"https://pith.science/pith/N3HMBDRCQBAPJLFMS2LZML4746.json","view_paper":"https://pith.science/paper/N3HMBDRC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1209.4919&json=true","fetch_graph":"https://pith.science/api/pith-number/N3HMBDRCQBAPJLFMS2LZML4746/graph.json","fetch_events":"https://pith.science/api/pith-number/N3HMBDRCQBAPJLFMS2LZML4746/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/N3HMBDRCQBAPJLFMS2LZML4746/action/timestamp_anchor","attest_storage":"https://pith.science/pith/N3HMBDRCQBAPJLFMS2LZML4746/action/storage_attestation","attest_author":"https://pith.science/pith/N3HMBDRCQBAPJLFMS2LZML4746/action/author_attestation","sign_citation":"https://pith.science/pith/N3HMBDRCQBAPJLFMS2LZML4746/action/citation_signature","submit_replication":"https://pith.science/pith/N3HMBDRCQBAPJLFMS2LZML4746/action/replication_record"}},"created_at":"2026-05-18T01:56:00.171386+00:00","updated_at":"2026-05-18T01:56:00.171386+00:00"}