{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:56ZER2QBZU26NS23WU4JI63BKH","short_pith_number":"pith:56ZER2QB","schema_version":"1.0","canonical_sha256":"efb248ea01cd35e6cb5bb538947b6151fb6307da270440abd229b52861dd2bd9","source":{"kind":"arxiv","id":"1505.03938","version":1},"attestation_state":"computed","paper":{"title":"SPDEs with two reflecting walls and two singular drifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jianliang Zhai, Juan Yang","submitted_at":"2015-05-15T01:50:22Z","abstract_excerpt":"We study SPDEs with two reflecting walls $\\Lambda^1$, $\\Lambda^2$ and two singular drifts $\\frac{c_1}{(X-\\Lambda^1)^{\\vartheta}}$, $\\frac{c_2}{(\\Lambda^2-X)^{\\vartheta}}$, driven by space-time white noise. First, we establish the existence and uniqueness of the solutions $X$ for $\\vartheta\\geq 0$. Second, we obtain the following pathwise properties of the solutions $X$. If $\\vartheta>3$, then a.s. $\\Lambda^1<X<\\Lambda^2$ for all $t\\geq0$; If $0<\\vartheta<3$, then $X$ hits $\\Lambda^1$ or $\\Lambda^2$ with positive probability in finite time. Thus $\\vartheta=3$ is the critical parameter for $X$ t"},"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":"1505.03938","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-15T01:50:22Z","cross_cats_sorted":[],"title_canon_sha256":"af7e3ab5e8654441b07531f62f5d2d0abeab519f136dcbf4ade1aab03b5a6e26","abstract_canon_sha256":"fd2464e3b4eeba6461e179b1ad617e180017f31cbd5081e234a452316c81cef9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:09:40.657349Z","signature_b64":"CXw8Wp6N/vD03uekf/yw9aKmvOYsSVyywS6kMYt0ZuuYLQn6aP3orZ0zWnpfWuQBTHiaFOmHfYklpR5s7HHCCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"efb248ea01cd35e6cb5bb538947b6151fb6307da270440abd229b52861dd2bd9","last_reissued_at":"2026-05-18T02:09:40.656644Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:09:40.656644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"SPDEs with two reflecting walls and two singular drifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jianliang Zhai, Juan Yang","submitted_at":"2015-05-15T01:50:22Z","abstract_excerpt":"We study SPDEs with two reflecting walls $\\Lambda^1$, $\\Lambda^2$ and two singular drifts $\\frac{c_1}{(X-\\Lambda^1)^{\\vartheta}}$, $\\frac{c_2}{(\\Lambda^2-X)^{\\vartheta}}$, driven by space-time white noise. First, we establish the existence and uniqueness of the solutions $X$ for $\\vartheta\\geq 0$. Second, we obtain the following pathwise properties of the solutions $X$. If $\\vartheta>3$, then a.s. $\\Lambda^1<X<\\Lambda^2$ for all $t\\geq0$; If $0<\\vartheta<3$, then $X$ hits $\\Lambda^1$ or $\\Lambda^2$ with positive probability in finite time. Thus $\\vartheta=3$ is the critical parameter for $X$ t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03938","kind":"arxiv","version":1},"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":"1505.03938","created_at":"2026-05-18T02:09:40.656746+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.03938v1","created_at":"2026-05-18T02:09:40.656746+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.03938","created_at":"2026-05-18T02:09:40.656746+00:00"},{"alias_kind":"pith_short_12","alias_value":"56ZER2QBZU26","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"56ZER2QBZU26NS23","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"56ZER2QB","created_at":"2026-05-18T12:29:05.191682+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/56ZER2QBZU26NS23WU4JI63BKH","json":"https://pith.science/pith/56ZER2QBZU26NS23WU4JI63BKH.json","graph_json":"https://pith.science/api/pith-number/56ZER2QBZU26NS23WU4JI63BKH/graph.json","events_json":"https://pith.science/api/pith-number/56ZER2QBZU26NS23WU4JI63BKH/events.json","paper":"https://pith.science/paper/56ZER2QB"},"agent_actions":{"view_html":"https://pith.science/pith/56ZER2QBZU26NS23WU4JI63BKH","download_json":"https://pith.science/pith/56ZER2QBZU26NS23WU4JI63BKH.json","view_paper":"https://pith.science/paper/56ZER2QB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.03938&json=true","fetch_graph":"https://pith.science/api/pith-number/56ZER2QBZU26NS23WU4JI63BKH/graph.json","fetch_events":"https://pith.science/api/pith-number/56ZER2QBZU26NS23WU4JI63BKH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/56ZER2QBZU26NS23WU4JI63BKH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/56ZER2QBZU26NS23WU4JI63BKH/action/storage_attestation","attest_author":"https://pith.science/pith/56ZER2QBZU26NS23WU4JI63BKH/action/author_attestation","sign_citation":"https://pith.science/pith/56ZER2QBZU26NS23WU4JI63BKH/action/citation_signature","submit_replication":"https://pith.science/pith/56ZER2QBZU26NS23WU4JI63BKH/action/replication_record"}},"created_at":"2026-05-18T02:09:40.656746+00:00","updated_at":"2026-05-18T02:09:40.656746+00:00"}