{"paper":{"title":"Superdiffusions with large mass creation --- construction and growth estimates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Janos Englander, Zhen-Qing Chen","submitted_at":"2017-06-29T17:23:43Z","abstract_excerpt":"Superdiffusions corresponding to differential operators of the form $\\LL u+\\beta u-\\alpha u^{2}$ with large mass creation term $\\beta$ are studied. Our construction for superdiffusions with large mass creations works for the branching mechanism $\\beta u-\\alpha u^{1+\\gamma},\\ 0<\\gamma<1,$ as well.\n  Let $D\\subseteq\\mathbb{R}^{d}$ be a domain in $\\R^d$. When $\\beta$ is large, the generalized principal eigenvalue $\\lambda_c$ of $L+\\beta$ in $D$ is typically infinite. Let $\\{T_{t},t\\ge0\\}$ denote the Schr\\\"odinger semigroup of $L+\\beta$ in $D$ with zero Dirichlet boundary condition. Under the mild"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.09864","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"}