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Lalley, Xinghua Zheng","submitted_at":"2011-11-28T14:39:08Z","abstract_excerpt":"We consider measure-valued processes $X=(X_t)$ that solve the following martingale problem: for a given initial measure $X_0$, and for all smooth, compactly supported test functions $\\varphi$, \\begin{eqnarray*}X_t(\\varphi )=X_0(\\varphi)+\\frac{1}{2}\\int _0^tX_s(\\Delta \\varphi )\\,ds+\\theta \\int_0^tX_s(\\varphi )\\,ds\\\\{}-\\int_0^tX_s(L_s\\varphi )\\,ds+M_t(\\varphi ).\\end{eqnarray*} Here $L_s(x)$ is the local time density process associated with $X$, and $M_t(\\varphi )$ is a martingale with quadratic variation $[M(\\varphi )]_t=\\int_0^tX_s(\\varphi ^2)\\,ds$. Such processes arise as scaling limits of SIR"},"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":"1111.6451","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-28T14:39:08Z","cross_cats_sorted":[],"title_canon_sha256":"f72561c47c098557f9609a50bb6262db0f8c8cc3ec34f579bb5a8d416d9ec76f","abstract_canon_sha256":"c28c1845c932b26d5c2456bceae14ade028a2c0c1fa759740775cbc22e23c2ee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:21.485073Z","signature_b64":"A2JItcbU3a7ISUF0omw55jQkztHEO3ZBfPfVJJvUYf+HeuBYD/nGKZMze6Z7dGGoyfvKSv4n0JnCdB11+0azBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54acbffad3e550c88094884b66c2b60eb79fc291d5e7427eaed2371f95188349","last_reissued_at":"2026-05-18T03:02:21.484276Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:21.484276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A phase transition for measure-valued SIR epidemic processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Edwin A. Perkins, Steven P. Lalley, Xinghua Zheng","submitted_at":"2011-11-28T14:39:08Z","abstract_excerpt":"We consider measure-valued processes $X=(X_t)$ that solve the following martingale problem: for a given initial measure $X_0$, and for all smooth, compactly supported test functions $\\varphi$, \\begin{eqnarray*}X_t(\\varphi )=X_0(\\varphi)+\\frac{1}{2}\\int _0^tX_s(\\Delta \\varphi )\\,ds+\\theta \\int_0^tX_s(\\varphi )\\,ds\\\\{}-\\int_0^tX_s(L_s\\varphi )\\,ds+M_t(\\varphi ).\\end{eqnarray*} Here $L_s(x)$ is the local time density process associated with $X$, and $M_t(\\varphi )$ is a martingale with quadratic variation $[M(\\varphi )]_t=\\int_0^tX_s(\\varphi ^2)\\,ds$. Such processes arise as scaling limits of SIR"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6451","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":"1111.6451","created_at":"2026-05-18T03:02:21.484455+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.6451v3","created_at":"2026-05-18T03:02:21.484455+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.6451","created_at":"2026-05-18T03:02:21.484455+00:00"},{"alias_kind":"pith_short_12","alias_value":"KSWL76WT4VIM","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_16","alias_value":"KSWL76WT4VIMRAEU","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_8","alias_value":"KSWL76WT","created_at":"2026-05-18T12:26:34.985390+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/KSWL76WT4VIMRAEURBFWNQVWB2","json":"https://pith.science/pith/KSWL76WT4VIMRAEURBFWNQVWB2.json","graph_json":"https://pith.science/api/pith-number/KSWL76WT4VIMRAEURBFWNQVWB2/graph.json","events_json":"https://pith.science/api/pith-number/KSWL76WT4VIMRAEURBFWNQVWB2/events.json","paper":"https://pith.science/paper/KSWL76WT"},"agent_actions":{"view_html":"https://pith.science/pith/KSWL76WT4VIMRAEURBFWNQVWB2","download_json":"https://pith.science/pith/KSWL76WT4VIMRAEURBFWNQVWB2.json","view_paper":"https://pith.science/paper/KSWL76WT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.6451&json=true","fetch_graph":"https://pith.science/api/pith-number/KSWL76WT4VIMRAEURBFWNQVWB2/graph.json","fetch_events":"https://pith.science/api/pith-number/KSWL76WT4VIMRAEURBFWNQVWB2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KSWL76WT4VIMRAEURBFWNQVWB2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KSWL76WT4VIMRAEURBFWNQVWB2/action/storage_attestation","attest_author":"https://pith.science/pith/KSWL76WT4VIMRAEURBFWNQVWB2/action/author_attestation","sign_citation":"https://pith.science/pith/KSWL76WT4VIMRAEURBFWNQVWB2/action/citation_signature","submit_replication":"https://pith.science/pith/KSWL76WT4VIMRAEURBFWNQVWB2/action/replication_record"}},"created_at":"2026-05-18T03:02:21.484455+00:00","updated_at":"2026-05-18T03:02:21.484455+00:00"}