{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:CJ2E5DLIRJIRKSNNFI6SZZ4RS2","short_pith_number":"pith:CJ2E5DLI","schema_version":"1.0","canonical_sha256":"12744e8d688a511549ad2a3d2ce7919698ce90b8e0b724dcf07c22443c493048","source":{"kind":"arxiv","id":"0810.2930","version":2},"attestation_state":"computed","paper":{"title":"Explicit formulas for Laplace transforms of certain functionals of some time inhomogeneous diffusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Gyula Pap, Matyas Barczy","submitted_at":"2008-10-16T15:23:24Z","abstract_excerpt":"We consider a process $(X_t)_{t\\in[0,T)}$ given by the SDE $dX_t = \\alpha b(t)X_t dt + \\sigma(t) dB_t$, $t\\in[0,T)$, with initial condition $X_0=0$, where $T\\in(0,\\infty]$, $\\alpha\\in R$, $(B_t)_{t\\in[0,T)}$ is a standard Wiener process, $b:[0,T)\\to R\\setminus\\{0\\}$ and $\\sigma:[0,T)\\to(0,\\infty)$ are continuously differentiable functions. Assuming that $b$ and $\\sigma$ satisfy a certain differential equation we derive an explicit formula for the joint Laplace transform of $\\int_0^t\\frac{b(s)^2}{\\sigma(s)^2}(X_s)^2 ds$ and $(X_t)^2$ for all $t\\in[0,T)$. As an application, we study asymptotic b"},"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":"0810.2930","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-10-16T15:23:24Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"3640f1dbabbd2f223190c5e05cb55f16ae53bf1d594baca18c99c806b72aa241","abstract_canon_sha256":"6add0adf44fa959ece096a5ed1d13268e0b00a2ac1972b7d24f5e63c057102af"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:06.449231Z","signature_b64":"s/5ScgWErZOc667DdUOxzlI/gRNdZGkpgdKBe+vG3R+h4Z6sVygnPtyqLQcHhNMqf7qu9YPB2kzuo/ivLJxRDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12744e8d688a511549ad2a3d2ce7919698ce90b8e0b724dcf07c22443c493048","last_reissued_at":"2026-05-18T04:24:06.448597Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:06.448597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Explicit formulas for Laplace transforms of certain functionals of some time inhomogeneous diffusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Gyula Pap, Matyas Barczy","submitted_at":"2008-10-16T15:23:24Z","abstract_excerpt":"We consider a process $(X_t)_{t\\in[0,T)}$ given by the SDE $dX_t = \\alpha b(t)X_t dt + \\sigma(t) dB_t$, $t\\in[0,T)$, with initial condition $X_0=0$, where $T\\in(0,\\infty]$, $\\alpha\\in R$, $(B_t)_{t\\in[0,T)}$ is a standard Wiener process, $b:[0,T)\\to R\\setminus\\{0\\}$ and $\\sigma:[0,T)\\to(0,\\infty)$ are continuously differentiable functions. Assuming that $b$ and $\\sigma$ satisfy a certain differential equation we derive an explicit formula for the joint Laplace transform of $\\int_0^t\\frac{b(s)^2}{\\sigma(s)^2}(X_s)^2 ds$ and $(X_t)^2$ for all $t\\in[0,T)$. As an application, we study asymptotic b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.2930","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":"0810.2930","created_at":"2026-05-18T04:24:06.448688+00:00"},{"alias_kind":"arxiv_version","alias_value":"0810.2930v2","created_at":"2026-05-18T04:24:06.448688+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.2930","created_at":"2026-05-18T04:24:06.448688+00:00"},{"alias_kind":"pith_short_12","alias_value":"CJ2E5DLIRJIR","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_16","alias_value":"CJ2E5DLIRJIRKSNN","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_8","alias_value":"CJ2E5DLI","created_at":"2026-05-18T12:25:57.157939+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/CJ2E5DLIRJIRKSNNFI6SZZ4RS2","json":"https://pith.science/pith/CJ2E5DLIRJIRKSNNFI6SZZ4RS2.json","graph_json":"https://pith.science/api/pith-number/CJ2E5DLIRJIRKSNNFI6SZZ4RS2/graph.json","events_json":"https://pith.science/api/pith-number/CJ2E5DLIRJIRKSNNFI6SZZ4RS2/events.json","paper":"https://pith.science/paper/CJ2E5DLI"},"agent_actions":{"view_html":"https://pith.science/pith/CJ2E5DLIRJIRKSNNFI6SZZ4RS2","download_json":"https://pith.science/pith/CJ2E5DLIRJIRKSNNFI6SZZ4RS2.json","view_paper":"https://pith.science/paper/CJ2E5DLI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0810.2930&json=true","fetch_graph":"https://pith.science/api/pith-number/CJ2E5DLIRJIRKSNNFI6SZZ4RS2/graph.json","fetch_events":"https://pith.science/api/pith-number/CJ2E5DLIRJIRKSNNFI6SZZ4RS2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CJ2E5DLIRJIRKSNNFI6SZZ4RS2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CJ2E5DLIRJIRKSNNFI6SZZ4RS2/action/storage_attestation","attest_author":"https://pith.science/pith/CJ2E5DLIRJIRKSNNFI6SZZ4RS2/action/author_attestation","sign_citation":"https://pith.science/pith/CJ2E5DLIRJIRKSNNFI6SZZ4RS2/action/citation_signature","submit_replication":"https://pith.science/pith/CJ2E5DLIRJIRKSNNFI6SZZ4RS2/action/replication_record"}},"created_at":"2026-05-18T04:24:06.448688+00:00","updated_at":"2026-05-18T04:24:06.448688+00:00"}