{"paper":{"title":"Strong law of large numbers for supercritical superprocesses under second moment condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Renming Song, Rui Zhang, Yan-Xia Ren, Zhen-Qing Chen","submitted_at":"2015-02-05T03:42:16Z","abstract_excerpt":"Suppose that $X=\\{X_t, t\\ge 0\\}$ is a supercritical superprocess on a locally compact separable metric space $(E, m)$. Suppose that the spatial motion of $X$ is a Hunt process satisfying certain conditions and that the branching mechanism is of the form $$ \\psi(x,\\lambda)=-a(x)\\lambda+b(x)\\lambda^2+\\int_{(0,+\\infty)}(e^{-\\lambda y}-1+\\lambda y)n(x,dy), \\quad x\\in E, \\quad\\lambda> 0, $$ where $a\\in \\mathcal{B}_b(E)$, $b\\in \\mathcal{B}_b^+(E)$ and $n$ is a kernel from $E$ to $(0,\\infty)$ satisfying $$\n  \\sup_{x\\in E}\\int_0^\\infty y^2 n(x,dy)<\\infty. $$ Put $T_tf(x)=\\mathbb{P}_{\\delta_x}< f,X_t>$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01426","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"}