{"paper":{"title":"Limit theorems for a class of critical superprocesses with stable branching","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Renming Song, Yan-Xia Ren, Zhenyao Sun","submitted_at":"2018-07-08T15:13:16Z","abstract_excerpt":"We consider a critical superprocess $\\{X;\\mathbf P_\\mu\\}$ with general spatial motion and spatially dependent stable branching mechanism with lowest stable index $\\gamma_0 > 1$. We first show that, under some conditions, $\\mathbf P_{\\mu}(\\|X_t\\|\\neq 0)$ converges to $0$ as $t\\to \\infty$ and is regularly varying with index $(\\gamma_0-1)^{-1}$. Then we show that, for a large class of non-negative testing functions $f$, the distribution of $\\{X_t(f);\\mathbf P_\\mu(\\cdot|\\|X_t\\|\\neq 0)\\}$, after appropriate rescaling, converges weakly to a positive random variable $\\mathbf z^{(\\gamma_0-1)}$ with La"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.02837","kind":"arxiv","version":2},"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"}