{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:COZVL3QRPHN3DDD3GP2AAHN2MO","short_pith_number":"pith:COZVL3QR","schema_version":"1.0","canonical_sha256":"13b355ee1179dbb18c7b33f4001dba63b7d26a72ba9e7d405a0e86dc9e0fd603","source":{"kind":"arxiv","id":"1807.08807","version":2},"attestation_state":"computed","paper":{"title":"First passage in an interval for fractional Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Kay Joerg Wiese","submitted_at":"2018-07-23T19:53:30Z","abstract_excerpt":"Be $X_t$ a random process starting at $x \\in [0,1]$ with absorbing boundary conditions at both ends of the interval. Denote $P_1(x)$ the probability to first exit at the upper boundary. For Brownian motion, $P_1(x)=x$, equivalent to $P_1'(x)=1$. For fractional Brownian motion with Hurst exponent $H$, we establish that $P_1'(x) = {\\cal N} [x(1-x)]^{\\frac1H -2} e^{\\epsilon {\\cal F}(x)+ {\\cal O}(\\epsilon^2)}$, where $\\epsilon=H-\\frac12$. The function ${\\cal F}(x)$ is analytic, and well approximated by its Taylor expansion, ${\\cal F}(x)\\simeq 16 (C-1) (x-1/2)^2 +{\\cal O}(x-1/2)^4$, where $C= 0.915"},"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":"1807.08807","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-07-23T19:53:30Z","cross_cats_sorted":[],"title_canon_sha256":"05f364be62897b1f1db0dabf17ff34108f3fd1679669f4a74b73a9591888e711","abstract_canon_sha256":"5f7cba3eff2e7e584f174dbd1073010f2ef5c081aeddc174a8a0b2cbae140ab8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:33.569158Z","signature_b64":"OkgTg12O0U/CZ9WuaAgpHkuVVsyO3o1hV7wi6g39cCkOL4uGL51okeHK7o3NNr1gsvAUf2Fk7iqfyafzRr4YCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13b355ee1179dbb18c7b33f4001dba63b7d26a72ba9e7d405a0e86dc9e0fd603","last_reissued_at":"2026-05-17T23:51:33.568462Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:33.568462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"First passage in an interval for fractional Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Kay Joerg Wiese","submitted_at":"2018-07-23T19:53:30Z","abstract_excerpt":"Be $X_t$ a random process starting at $x \\in [0,1]$ with absorbing boundary conditions at both ends of the interval. Denote $P_1(x)$ the probability to first exit at the upper boundary. For Brownian motion, $P_1(x)=x$, equivalent to $P_1'(x)=1$. For fractional Brownian motion with Hurst exponent $H$, we establish that $P_1'(x) = {\\cal N} [x(1-x)]^{\\frac1H -2} e^{\\epsilon {\\cal F}(x)+ {\\cal O}(\\epsilon^2)}$, where $\\epsilon=H-\\frac12$. The function ${\\cal F}(x)$ is analytic, and well approximated by its Taylor expansion, ${\\cal F}(x)\\simeq 16 (C-1) (x-1/2)^2 +{\\cal O}(x-1/2)^4$, where $C= 0.915"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08807","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1807.08807","created_at":"2026-05-17T23:51:33.568577+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.08807v2","created_at":"2026-05-17T23:51:33.568577+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.08807","created_at":"2026-05-17T23:51:33.568577+00:00"},{"alias_kind":"pith_short_12","alias_value":"COZVL3QRPHN3","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_16","alias_value":"COZVL3QRPHN3DDD3","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_8","alias_value":"COZVL3QR","created_at":"2026-05-18T12:32:16.446611+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.02433","citing_title":"Aging Record Statistics in Saturating Self-Interacting Random Walks","ref_index":50,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/COZVL3QRPHN3DDD3GP2AAHN2MO","json":"https://pith.science/pith/COZVL3QRPHN3DDD3GP2AAHN2MO.json","graph_json":"https://pith.science/api/pith-number/COZVL3QRPHN3DDD3GP2AAHN2MO/graph.json","events_json":"https://pith.science/api/pith-number/COZVL3QRPHN3DDD3GP2AAHN2MO/events.json","paper":"https://pith.science/paper/COZVL3QR"},"agent_actions":{"view_html":"https://pith.science/pith/COZVL3QRPHN3DDD3GP2AAHN2MO","download_json":"https://pith.science/pith/COZVL3QRPHN3DDD3GP2AAHN2MO.json","view_paper":"https://pith.science/paper/COZVL3QR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.08807&json=true","fetch_graph":"https://pith.science/api/pith-number/COZVL3QRPHN3DDD3GP2AAHN2MO/graph.json","fetch_events":"https://pith.science/api/pith-number/COZVL3QRPHN3DDD3GP2AAHN2MO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/COZVL3QRPHN3DDD3GP2AAHN2MO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/COZVL3QRPHN3DDD3GP2AAHN2MO/action/storage_attestation","attest_author":"https://pith.science/pith/COZVL3QRPHN3DDD3GP2AAHN2MO/action/author_attestation","sign_citation":"https://pith.science/pith/COZVL3QRPHN3DDD3GP2AAHN2MO/action/citation_signature","submit_replication":"https://pith.science/pith/COZVL3QRPHN3DDD3GP2AAHN2MO/action/replication_record"}},"created_at":"2026-05-17T23:51:33.568577+00:00","updated_at":"2026-05-17T23:51:33.568577+00:00"}