Ergodic behavior of locally regulated branching populations

• 成果类型: Article
• 署名作者: Hutzenthaler, M.; Wakolbinger, A.
• 署名单位: Goethe University Frankfurt
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051606000000745
• 发表日期: 2007
• 页码: 474-501
• 关键词: interacting diffusions; systems; equation; THEOREMS

摘要

For a class of processes modeling the evolution of a spatially structured population with migration and a logistic local regulation of the reproduction dynamics, we show convergence to an upper invariant measure from a suitable class of initial distributions. It follows from recent work of Alison Etheridge that this upper invariant measure is nontrivial for sufficiently large super-criticality in the reproduction. For sufficiently small super-criticality, we prove local extinction by comparison with a mean field model. This latter result extends also to more general local reproduction regulations.