{"paper":{"title":"Semigroup approach to birth-and-death stochastic dynamics in continuum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DS","math.MP"],"primary_cat":"math.FA","authors_text":"Dmitri Finkelshtein, Oleksandr Kutoviy, Yuri Kondratiev","submitted_at":"2011-09-23T14:49:43Z","abstract_excerpt":"We describe a general approach to the construction of a state evolution corresponding to the Markov generator of a spatial birth-and-death dynamics in $\\mathbb{R}^d$. We present conditions on the birth-and-death intensities which are sufficient for the existence of an evolution as a strongly continuous semigroup in a proper Banach space of correlation functions satisfying the Ruelle bound. The convergence of a Vlasov-type scaling for the corresponding stochastic dynamics is considered."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5094","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"}