{"paper":{"title":"Spatial CLT for the supercritical Ornstein-Uhlenbeck superprocess","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Piotr Mi{\\l}o\\'s","submitted_at":"2012-03-29T20:11:59Z","abstract_excerpt":"In this paper we consider a superprocess being a measure-valued diffusion corresponding to the equation $u_{t}=Lu+\\alpha u-\\beta u^{2}$, where $L$ is the infinitesimal operator of the \\emph{Ornstein-Uhlenbeck process} and $\\beta>0,\\:\\alpha>0$. The latter condition implies that the process is \\emph{supercritical,} i.e. its total mass grows exponentially. This system is known to fulfill a law of large numbers. In the paper we prove the corresponding \\emph{central limit theorem}. The limit and the CLT normalization fall into three qualitatively different classes. In what we call the small growth "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.6661","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"}