{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:CJ2E5DLIRJIRKSNNFI6SZZ4RS2","short_pith_number":"pith:CJ2E5DLI","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"},"canonical_sha256":"12744e8d688a511549ad2a3d2ce7919698ce90b8e0b724dcf07c22443c493048","source":{"kind":"arxiv","id":"0810.2930","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.2930","created_at":"2026-05-18T04:24:06Z"},{"alias_kind":"arxiv_version","alias_value":"0810.2930v2","created_at":"2026-05-18T04:24:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.2930","created_at":"2026-05-18T04:24:06Z"},{"alias_kind":"pith_short_12","alias_value":"CJ2E5DLIRJIR","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"CJ2E5DLIRJIRKSNN","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"CJ2E5DLI","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:CJ2E5DLIRJIRKSNNFI6SZZ4RS2","target":"record","payload":{"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"},"canonical_sha256":"12744e8d688a511549ad2a3d2ce7919698ce90b8e0b724dcf07c22443c493048","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"},"source_kind":"arxiv","source_id":"0810.2930","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:24:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LGpy3oHIdijh20pu1uq1JbVXx7zk+USP+0HdmZzzL4TUnIukZq8A2xZrXucJlCRaqb2FA3RhUDo8Y5jAMtYOBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T19:24:30.290682Z"},"content_sha256":"baddb6e809acf48fbd511936326ed6f153a0cac163f114516ff9ca8637bb736a","schema_version":"1.0","event_id":"sha256:baddb6e809acf48fbd511936326ed6f153a0cac163f114516ff9ca8637bb736a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:CJ2E5DLIRJIRKSNNFI6SZZ4RS2","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:24:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N/SDzb4TOyZwTkBoVQmSn1PoMfdPMlmf+FbgCgiLOkiE3fQJR4n3R43QFxzVW+lHDQnW+GhhHESxDeOitIZtAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T19:24:30.291349Z"},"content_sha256":"546542d352c8be12571f69b9b882678c01b5418494fb845df578f2b211dde0a7","schema_version":"1.0","event_id":"sha256:546542d352c8be12571f69b9b882678c01b5418494fb845df578f2b211dde0a7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CJ2E5DLIRJIRKSNNFI6SZZ4RS2/bundle.json","state_url":"https://pith.science/pith/CJ2E5DLIRJIRKSNNFI6SZZ4RS2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CJ2E5DLIRJIRKSNNFI6SZZ4RS2/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T19:24:30Z","links":{"resolver":"https://pith.science/pith/CJ2E5DLIRJIRKSNNFI6SZZ4RS2","bundle":"https://pith.science/pith/CJ2E5DLIRJIRKSNNFI6SZZ4RS2/bundle.json","state":"https://pith.science/pith/CJ2E5DLIRJIRKSNNFI6SZZ4RS2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CJ2E5DLIRJIRKSNNFI6SZZ4RS2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:CJ2E5DLIRJIRKSNNFI6SZZ4RS2","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6add0adf44fa959ece096a5ed1d13268e0b00a2ac1972b7d24f5e63c057102af","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-10-16T15:23:24Z","title_canon_sha256":"3640f1dbabbd2f223190c5e05cb55f16ae53bf1d594baca18c99c806b72aa241"},"schema_version":"1.0","source":{"id":"0810.2930","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.2930","created_at":"2026-05-18T04:24:06Z"},{"alias_kind":"arxiv_version","alias_value":"0810.2930v2","created_at":"2026-05-18T04:24:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.2930","created_at":"2026-05-18T04:24:06Z"},{"alias_kind":"pith_short_12","alias_value":"CJ2E5DLIRJIR","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"CJ2E5DLIRJIRKSNN","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"CJ2E5DLI","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:546542d352c8be12571f69b9b882678c01b5418494fb845df578f2b211dde0a7","target":"graph","created_at":"2026-05-18T04:24:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Gyula Pap, Matyas Barczy","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-10-16T15:23:24Z","title":"Explicit formulas for Laplace transforms of certain functionals of some time inhomogeneous diffusions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.2930","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:baddb6e809acf48fbd511936326ed6f153a0cac163f114516ff9ca8637bb736a","target":"record","created_at":"2026-05-18T04:24:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6add0adf44fa959ece096a5ed1d13268e0b00a2ac1972b7d24f5e63c057102af","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-10-16T15:23:24Z","title_canon_sha256":"3640f1dbabbd2f223190c5e05cb55f16ae53bf1d594baca18c99c806b72aa241"},"schema_version":"1.0","source":{"id":"0810.2930","kind":"arxiv","version":2}},"canonical_sha256":"12744e8d688a511549ad2a3d2ce7919698ce90b8e0b724dcf07c22443c493048","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12744e8d688a511549ad2a3d2ce7919698ce90b8e0b724dcf07c22443c493048","first_computed_at":"2026-05-18T04:24:06.448597Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:06.448597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s/5ScgWErZOc667DdUOxzlI/gRNdZGkpgdKBe+vG3R+h4Z6sVygnPtyqLQcHhNMqf7qu9YPB2kzuo/ivLJxRDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:06.449231Z","signed_message":"canonical_sha256_bytes"},"source_id":"0810.2930","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:baddb6e809acf48fbd511936326ed6f153a0cac163f114516ff9ca8637bb736a","sha256:546542d352c8be12571f69b9b882678c01b5418494fb845df578f2b211dde0a7"],"state_sha256":"5ff77f355499864f6b12d09a9b1092dbda84276f225009487acc0c7e71e258d4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"US0skSBuPHnZIAMPOPIrYPEmm6vdOZvgMuWYN6FB3Rh4H24vy8VYjiTVXXKs9NFgCVurvQwiTY4jXKl9RTT0Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T19:24:30.294721Z","bundle_sha256":"b0b4b7d464d65ef7df33037794bc48eb8c59104f37b2d7234c4dcb3b9c3e7db7"}}