{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:4W4ILY6JIBGZZK6IAZXLRROT2O","short_pith_number":"pith:4W4ILY6J","schema_version":"1.0","canonical_sha256":"e5b885e3c9404d9cabc8066eb8c5d3d3be95543c9246752b9f98c61cc7d2b693","source":{"kind":"arxiv","id":"1804.10222","version":1},"attestation_state":"computed","paper":{"title":"A generator approach to stochastic monotonicity and propagation of order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Moritz Schauer, Richard C. Kraaij","submitted_at":"2018-04-26T18:15:46Z","abstract_excerpt":"We study stochastic monotonicity and propagation of order for Markov processes with respect to stochastic integral orders characterized by cones of functions satisfying $\\Phi f \\geq 0$ for some linear operator $\\Phi$.\n  We introduce a new functional analytic technique based on the generator $A$ of a Markov process and its resolvent. We show that the existence of an operator $B$ with positive resolvent such that $\\Phi A - B \\Phi$ is a positive operator for a large enough class of functions implies stochastic monotonicity. This establishes a technique for proving stochastic monotonicity and prop"},"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":"1804.10222","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-04-26T18:15:46Z","cross_cats_sorted":[],"title_canon_sha256":"cc33c4f817ad0f894570e1b5c98ca1e74fb983646205bef7f6082cd38f32322a","abstract_canon_sha256":"316daabda92d6eebe49cf57d460f51c5275be523559e289eb492b48fcd27af09"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:21.426877Z","signature_b64":"jPwlEajaQPfJkaCQZidSPu3ho0YP1Jcu4b6b/79A15RdKY4+FPyv1KUpXy1ZkJb78OChO/hYJlIDT6O0cYQcCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5b885e3c9404d9cabc8066eb8c5d3d3be95543c9246752b9f98c61cc7d2b693","last_reissued_at":"2026-05-18T00:17:21.426074Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:21.426074Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A generator approach to stochastic monotonicity and propagation of order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Moritz Schauer, Richard C. Kraaij","submitted_at":"2018-04-26T18:15:46Z","abstract_excerpt":"We study stochastic monotonicity and propagation of order for Markov processes with respect to stochastic integral orders characterized by cones of functions satisfying $\\Phi f \\geq 0$ for some linear operator $\\Phi$.\n  We introduce a new functional analytic technique based on the generator $A$ of a Markov process and its resolvent. We show that the existence of an operator $B$ with positive resolvent such that $\\Phi A - B \\Phi$ is a positive operator for a large enough class of functions implies stochastic monotonicity. This establishes a technique for proving stochastic monotonicity and prop"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10222","kind":"arxiv","version":1},"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":"1804.10222","created_at":"2026-05-18T00:17:21.426201+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.10222v1","created_at":"2026-05-18T00:17:21.426201+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.10222","created_at":"2026-05-18T00:17:21.426201+00:00"},{"alias_kind":"pith_short_12","alias_value":"4W4ILY6JIBGZ","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_16","alias_value":"4W4ILY6JIBGZZK6I","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_8","alias_value":"4W4ILY6J","created_at":"2026-05-18T12:32:05.422762+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"1906.09656","citing_title":"The \"Red Radio Ring\": Ionised and Molecular Gas in a Starburst/Active Galactic Nucleus at $z \\sim 2.55$","ref_index":129,"is_internal_anchor":true},{"citing_arxiv_id":"2503.21724","citing_title":"Ram-Pressure Stripping Caught in Action in a Forming Cluster at $z \\sim 2.5$","ref_index":48,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4W4ILY6JIBGZZK6IAZXLRROT2O","json":"https://pith.science/pith/4W4ILY6JIBGZZK6IAZXLRROT2O.json","graph_json":"https://pith.science/api/pith-number/4W4ILY6JIBGZZK6IAZXLRROT2O/graph.json","events_json":"https://pith.science/api/pith-number/4W4ILY6JIBGZZK6IAZXLRROT2O/events.json","paper":"https://pith.science/paper/4W4ILY6J"},"agent_actions":{"view_html":"https://pith.science/pith/4W4ILY6JIBGZZK6IAZXLRROT2O","download_json":"https://pith.science/pith/4W4ILY6JIBGZZK6IAZXLRROT2O.json","view_paper":"https://pith.science/paper/4W4ILY6J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.10222&json=true","fetch_graph":"https://pith.science/api/pith-number/4W4ILY6JIBGZZK6IAZXLRROT2O/graph.json","fetch_events":"https://pith.science/api/pith-number/4W4ILY6JIBGZZK6IAZXLRROT2O/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4W4ILY6JIBGZZK6IAZXLRROT2O/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4W4ILY6JIBGZZK6IAZXLRROT2O/action/storage_attestation","attest_author":"https://pith.science/pith/4W4ILY6JIBGZZK6IAZXLRROT2O/action/author_attestation","sign_citation":"https://pith.science/pith/4W4ILY6JIBGZZK6IAZXLRROT2O/action/citation_signature","submit_replication":"https://pith.science/pith/4W4ILY6JIBGZZK6IAZXLRROT2O/action/replication_record"}},"created_at":"2026-05-18T00:17:21.426201+00:00","updated_at":"2026-05-18T00:17:21.426201+00:00"}