{"paper":{"title":"The compact support property for measure-valued processes","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Janos Englander, Ross G. Pinsky","submitted_at":"2005-04-19T15:55:36Z","abstract_excerpt":"The purpose of this article is to give a rather thorough understanding of the compact support property for measure-valued processes corresponding to semi-linear equations of the form \\[ \\begin{aligned}& u_t=Lu+\\beta u-\\alpha u^p \\text{in} R^d\\times (0,\\infty), p\\in(1,2]; &u(x,0)=f(x) \\text{in} R^d; &u(x,t)\\ge0 \\text{in} R^d\\times[0,\\infty). \\end{aligned} \\] In particular, we shall investigate how the interplay between the underlying motion (the diffusion process corresponding to $L$) and the branching affects the compact support property. In \\cite{EP99}, the compact support property was shown "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0504391","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"}