{"paper":{"title":"Lebesgue approximation of $(2,\\beta)$-superprocesses","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Xin He","submitted_at":"2012-01-31T04:29:21Z","abstract_excerpt":"Let $\\xi=(\\xi_t)$ be a locally finite $(2,\\beta)$-superprocess in $\\RR^d$ with $\\beta<1$ and $d>2/\\beta$. Then for any fixed $t>0$, the random measure $\\xi_t$ can be a.s. approximated by suitably normalized restrictions of Lebesgue measure to the $\\varepsilon$-neighborhoods of ${\\rm supp}\\,\\xi_t$. This extends the Lebesgue approximation of Dawson-Watanabe superprocesses. Our proof is based on a truncation of $(\\alpha,\\beta)$-superprocesses and uses bounds and asymptotics of hitting probabilities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.6437","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"}