The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 17, Number 2 (2007), 474-501.
Ergodic behavior of locally regulated branching populations
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.
Ann. Appl. Probab., Volume 17, Number 2 (2007), 474-501.
First available in Project Euclid: 19 March 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60J60: Diffusion processes [See also 58J65] 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 92D25: Population dynamics (general)
Hutzenthaler, M.; Wakolbinger, A. Ergodic behavior of locally regulated branching populations. Ann. Appl. Probab. 17 (2007), no. 2, 474--501. doi:10.1214/105051606000000745. https://projecteuclid.org/euclid.aoap/1174323254