{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:455PVD2JWVHLU6JT3COIEDM2YE","short_pith_number":"pith:455PVD2J","schema_version":"1.0","canonical_sha256":"e77afa8f49b54eba7933d89c820d9ac10b341b120330a8baf33472d6ecff817a","source":{"kind":"arxiv","id":"1301.6998","version":3},"attestation_state":"computed","paper":{"title":"On solutions of Kolmogorov's equations for jump Markov processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Albert N. Shiryaev, Eugene A. Feinberg, Manasa Mandava","submitted_at":"2013-01-29T17:44:11Z","abstract_excerpt":"This paper studies three ways to construct a nonhomogeneous jump Markov process: (i) via a compensator of the random measure of a multivariate point process, (ii) as a minimal solution of the backward Kolmogorov equation, and (iii) as a minimal solution of the forward Kolmogorov equation. The main conclusion of this paper is that, for a given measurable transition intensity, commonly called a Q-function, all these constructions define the same transition function. If this transition function is regular, that is, the probability of accumulation of jumps is zero, then this transition function is"},"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":"1301.6998","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-29T17:44:11Z","cross_cats_sorted":[],"title_canon_sha256":"0f5c8dd9160e54b14e254d912934de16e9b40a1156b61b140a4b94d65f35384f","abstract_canon_sha256":"91981838501015a071afd809a6be1879d7c32a04d13431ca2194a8a0304b3dc7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:28:45.457203Z","signature_b64":"ZzY31n1fQtrSPvSTZm4THyNY3SxIAqzvDaYNfhEypZ/Q2xQ82CJIQu5HUS2wW7Kf4sQWZD+UWWxP5CVtge8RCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e77afa8f49b54eba7933d89c820d9ac10b341b120330a8baf33472d6ecff817a","last_reissued_at":"2026-05-18T03:28:45.456357Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:28:45.456357Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On solutions of Kolmogorov's equations for jump Markov processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Albert N. Shiryaev, Eugene A. Feinberg, Manasa Mandava","submitted_at":"2013-01-29T17:44:11Z","abstract_excerpt":"This paper studies three ways to construct a nonhomogeneous jump Markov process: (i) via a compensator of the random measure of a multivariate point process, (ii) as a minimal solution of the backward Kolmogorov equation, and (iii) as a minimal solution of the forward Kolmogorov equation. The main conclusion of this paper is that, for a given measurable transition intensity, commonly called a Q-function, all these constructions define the same transition function. If this transition function is regular, that is, the probability of accumulation of jumps is zero, then this transition function is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.6998","kind":"arxiv","version":3},"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":"1301.6998","created_at":"2026-05-18T03:28:45.456495+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.6998v3","created_at":"2026-05-18T03:28:45.456495+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.6998","created_at":"2026-05-18T03:28:45.456495+00:00"},{"alias_kind":"pith_short_12","alias_value":"455PVD2JWVHL","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_16","alias_value":"455PVD2JWVHLU6JT","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_8","alias_value":"455PVD2J","created_at":"2026-05-18T12:27:32.513160+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/455PVD2JWVHLU6JT3COIEDM2YE","json":"https://pith.science/pith/455PVD2JWVHLU6JT3COIEDM2YE.json","graph_json":"https://pith.science/api/pith-number/455PVD2JWVHLU6JT3COIEDM2YE/graph.json","events_json":"https://pith.science/api/pith-number/455PVD2JWVHLU6JT3COIEDM2YE/events.json","paper":"https://pith.science/paper/455PVD2J"},"agent_actions":{"view_html":"https://pith.science/pith/455PVD2JWVHLU6JT3COIEDM2YE","download_json":"https://pith.science/pith/455PVD2JWVHLU6JT3COIEDM2YE.json","view_paper":"https://pith.science/paper/455PVD2J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.6998&json=true","fetch_graph":"https://pith.science/api/pith-number/455PVD2JWVHLU6JT3COIEDM2YE/graph.json","fetch_events":"https://pith.science/api/pith-number/455PVD2JWVHLU6JT3COIEDM2YE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/455PVD2JWVHLU6JT3COIEDM2YE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/455PVD2JWVHLU6JT3COIEDM2YE/action/storage_attestation","attest_author":"https://pith.science/pith/455PVD2JWVHLU6JT3COIEDM2YE/action/author_attestation","sign_citation":"https://pith.science/pith/455PVD2JWVHLU6JT3COIEDM2YE/action/citation_signature","submit_replication":"https://pith.science/pith/455PVD2JWVHLU6JT3COIEDM2YE/action/replication_record"}},"created_at":"2026-05-18T03:28:45.456495+00:00","updated_at":"2026-05-18T03:28:45.456495+00:00"}