Abstract
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.
Citation
M. Hutzenthaler. A. Wakolbinger. "Ergodic behavior of locally regulated branching populations." Ann. Appl. Probab. 17 (2) 474 - 501, April 2007. https://doi.org/10.1214/105051606000000745
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