{"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"}