{"paper":{"title":"Strong law of large number of a class of super-diffusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Renming Song, Rong-Li Liu, Yan-Xia Ren","submitted_at":"2011-02-17T19:34:10Z","abstract_excerpt":"In this paper we prove that, under certain conditions, a strong law of large numbers holds for a class of super-diffusions $X$ corresponding to the evolution equation $\\partial_t u_t=L u_t+\\beta u_t-\\psi(u_t)$ on a bounded domain $D$ in $\\R^d$, where $L$ is the generator of the underlying diffusion and the branching mechanism\n  $\\psi(x,\\lambda)=1/2\\alpha(x)\\lambda^2+\\int_0^\\infty (e^{-\\lambda r}-1+\\lambda r)n(x, {\\rm d}r)$ satisfies $\\sup_{x\\in D}\\int_0^\\infty (r\\wedge r^2) n(x,{\\rm d}r)<\\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3668","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"}