{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:4NAH447VFONFHC4CVXSBHRZYN3","short_pith_number":"pith:4NAH447V","schema_version":"1.0","canonical_sha256":"e3407e73f52b9a538b82ade413c7386ee8f9998d020ed7d4b734c988b6ef7bfe","source":{"kind":"arxiv","id":"1112.0430","version":2},"attestation_state":"computed","paper":{"title":"When a Stochastic Exponential is a True Martingale. Extension of a Method of Bene^s","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"F. Klebaner, R. Liptser","submitted_at":"2011-12-02T11:45:19Z","abstract_excerpt":"Let $\\mathfrak{z}$ be a stochastic exponential, i.e., $\\mathfrak{z}_t=1+\\int_0^t\\mathfrak{z}_{s-}dM_s$, of a local martingale $M$ with jumps $\\triangle M_t>-1$. Then $\\mathfrak{z}$ is a nonnegative local martingale with $\\E\\mathfrak{z}_t\\le 1$. If $\\E\\mathfrak{z}_T= 1$, then $\\mathfrak{z}$ is a martingale on the time interval $[0,T]$. Martingale property plays an important role in many applications. It is therefore of interest to give natural and easy verifiable conditions for the martingale property. In this paper, the property $\\E\\mathfrak{z}_{_T}=1$ is verified with the so-called linear gro"},"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":"1112.0430","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-12-02T11:45:19Z","cross_cats_sorted":[],"title_canon_sha256":"1ec6583aea8ddb862e4e277d155e27fc90edc61543ed14ba8b8a166973df788a","abstract_canon_sha256":"546a80efba83a111a5e8d928bc7a4a8a2e592113c757249a5999e642bb93def3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:24.602571Z","signature_b64":"/4RLLotlkOfI2ATCobmqvFeHLC30gv5JqtcEGOoWQ5mJxuOsTwM4KLieLEqVdY1GTK3SXAUJ+nM0mQCldkYHCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e3407e73f52b9a538b82ade413c7386ee8f9998d020ed7d4b734c988b6ef7bfe","last_reissued_at":"2026-05-18T03:01:24.601864Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:24.601864Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"When a Stochastic Exponential is a True Martingale. Extension of a Method of Bene^s","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"F. Klebaner, R. Liptser","submitted_at":"2011-12-02T11:45:19Z","abstract_excerpt":"Let $\\mathfrak{z}$ be a stochastic exponential, i.e., $\\mathfrak{z}_t=1+\\int_0^t\\mathfrak{z}_{s-}dM_s$, of a local martingale $M$ with jumps $\\triangle M_t>-1$. Then $\\mathfrak{z}$ is a nonnegative local martingale with $\\E\\mathfrak{z}_t\\le 1$. If $\\E\\mathfrak{z}_T= 1$, then $\\mathfrak{z}$ is a martingale on the time interval $[0,T]$. Martingale property plays an important role in many applications. It is therefore of interest to give natural and easy verifiable conditions for the martingale property. In this paper, the property $\\E\\mathfrak{z}_{_T}=1$ is verified with the so-called linear gro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0430","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":"1112.0430","created_at":"2026-05-18T03:01:24.601977+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.0430v2","created_at":"2026-05-18T03:01:24.601977+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.0430","created_at":"2026-05-18T03:01:24.601977+00:00"},{"alias_kind":"pith_short_12","alias_value":"4NAH447VFONF","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_16","alias_value":"4NAH447VFONFHC4C","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_8","alias_value":"4NAH447V","created_at":"2026-05-18T12:26:20.644004+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/4NAH447VFONFHC4CVXSBHRZYN3","json":"https://pith.science/pith/4NAH447VFONFHC4CVXSBHRZYN3.json","graph_json":"https://pith.science/api/pith-number/4NAH447VFONFHC4CVXSBHRZYN3/graph.json","events_json":"https://pith.science/api/pith-number/4NAH447VFONFHC4CVXSBHRZYN3/events.json","paper":"https://pith.science/paper/4NAH447V"},"agent_actions":{"view_html":"https://pith.science/pith/4NAH447VFONFHC4CVXSBHRZYN3","download_json":"https://pith.science/pith/4NAH447VFONFHC4CVXSBHRZYN3.json","view_paper":"https://pith.science/paper/4NAH447V","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.0430&json=true","fetch_graph":"https://pith.science/api/pith-number/4NAH447VFONFHC4CVXSBHRZYN3/graph.json","fetch_events":"https://pith.science/api/pith-number/4NAH447VFONFHC4CVXSBHRZYN3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4NAH447VFONFHC4CVXSBHRZYN3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4NAH447VFONFHC4CVXSBHRZYN3/action/storage_attestation","attest_author":"https://pith.science/pith/4NAH447VFONFHC4CVXSBHRZYN3/action/author_attestation","sign_citation":"https://pith.science/pith/4NAH447VFONFHC4CVXSBHRZYN3/action/citation_signature","submit_replication":"https://pith.science/pith/4NAH447VFONFHC4CVXSBHRZYN3/action/replication_record"}},"created_at":"2026-05-18T03:01:24.601977+00:00","updated_at":"2026-05-18T03:01:24.601977+00:00"}