{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:DQALOA3KMPIMIJ5L6NWRBMX3QL","short_pith_number":"pith:DQALOA3K","schema_version":"1.0","canonical_sha256":"1c00b7036a63d0c427abf36d10b2fb82ed38925f4e9a582ab7a3c3747d7efc74","source":{"kind":"arxiv","id":"1703.07963","version":4},"attestation_state":"computed","paper":{"title":"A Donsker-type Theorem for Log-likelihood Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hanchao Wang, Zhonggen Su","submitted_at":"2017-03-23T08:37:14Z","abstract_excerpt":"Let $(\\Omega, \\mathcal{F}, (\\mathcal{F})_{t\\ge 0}, P)$ be a complete stochastic basis, $X$ a semimartingale with predictable compensator $(B, C, \\nu)$. Consider a family of probability measures $\\mathbf{P}=( {P}^{n, \\psi}, \\psi\\in \\Psi, n\\ge 1)$, where $\\Psi$ is an index set, $ {P}^{n, \\psi}\\stackrel {loc} \\ll{P}$, and denote the likelihood ratio process by $Z_t^{n, \\psi} =\\frac{dP^{n, \\psi}|_{\\mathcal{F}_t}}{d P|_{\\mathcal{F}_t}}$. Under some regularity conditions in terms of logarithm entropy and Hellinger processes, we prove that $\\log Z_t^{n}$ converges weakly to a Gaussian process in $\\el"},"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":"1703.07963","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-03-23T08:37:14Z","cross_cats_sorted":[],"title_canon_sha256":"ff5aac7a0b1e2198d0f3baf5443135ebdbdfffad15120e8bac40ca8982cf5cc2","abstract_canon_sha256":"dc953418dfb5d01bbfd1cbb37f76d1accc739a3bb2e20c35abdfbd1c51eae83a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:28.704686Z","signature_b64":"I3sSPY31mKUoZ34xywVUa/Wn1oMHeijz62W8OH5mTMIOUtmZ482tKZ+ow5YTkKQGnb7VZKa+fzFhy9q6bH5RBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c00b7036a63d0c427abf36d10b2fb82ed38925f4e9a582ab7a3c3747d7efc74","last_reissued_at":"2026-05-17T23:43:28.703999Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:28.703999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Donsker-type Theorem for Log-likelihood Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hanchao Wang, Zhonggen Su","submitted_at":"2017-03-23T08:37:14Z","abstract_excerpt":"Let $(\\Omega, \\mathcal{F}, (\\mathcal{F})_{t\\ge 0}, P)$ be a complete stochastic basis, $X$ a semimartingale with predictable compensator $(B, C, \\nu)$. Consider a family of probability measures $\\mathbf{P}=( {P}^{n, \\psi}, \\psi\\in \\Psi, n\\ge 1)$, where $\\Psi$ is an index set, $ {P}^{n, \\psi}\\stackrel {loc} \\ll{P}$, and denote the likelihood ratio process by $Z_t^{n, \\psi} =\\frac{dP^{n, \\psi}|_{\\mathcal{F}_t}}{d P|_{\\mathcal{F}_t}}$. Under some regularity conditions in terms of logarithm entropy and Hellinger processes, we prove that $\\log Z_t^{n}$ converges weakly to a Gaussian process in $\\el"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07963","kind":"arxiv","version":4},"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":"1703.07963","created_at":"2026-05-17T23:43:28.704101+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.07963v4","created_at":"2026-05-17T23:43:28.704101+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.07963","created_at":"2026-05-17T23:43:28.704101+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/DQALOA3KMPIMIJ5L6NWRBMX3QL","json":"https://pith.science/pith/DQALOA3KMPIMIJ5L6NWRBMX3QL.json","graph_json":"https://pith.science/api/pith-number/DQALOA3KMPIMIJ5L6NWRBMX3QL/graph.json","events_json":"https://pith.science/api/pith-number/DQALOA3KMPIMIJ5L6NWRBMX3QL/events.json","paper":"https://pith.science/paper/DQALOA3K"},"agent_actions":{"view_html":"https://pith.science/pith/DQALOA3KMPIMIJ5L6NWRBMX3QL","download_json":"https://pith.science/pith/DQALOA3KMPIMIJ5L6NWRBMX3QL.json","view_paper":"https://pith.science/paper/DQALOA3K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.07963&json=true","fetch_graph":"https://pith.science/api/pith-number/DQALOA3KMPIMIJ5L6NWRBMX3QL/graph.json","fetch_events":"https://pith.science/api/pith-number/DQALOA3KMPIMIJ5L6NWRBMX3QL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DQALOA3KMPIMIJ5L6NWRBMX3QL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DQALOA3KMPIMIJ5L6NWRBMX3QL/action/storage_attestation","attest_author":"https://pith.science/pith/DQALOA3KMPIMIJ5L6NWRBMX3QL/action/author_attestation","sign_citation":"https://pith.science/pith/DQALOA3KMPIMIJ5L6NWRBMX3QL/action/citation_signature","submit_replication":"https://pith.science/pith/DQALOA3KMPIMIJ5L6NWRBMX3QL/action/replication_record"}},"created_at":"2026-05-17T23:43:28.704101+00:00","updated_at":"2026-05-17T23:43:28.704101+00:00"}