The Annals of Applied Probability

Ergodic behavior of locally regulated branching populations

M. Hutzenthaler and A. Wakolbinger

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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.

Article information

Source
Ann. Appl. Probab., Volume 17, Number 2 (2007), 474-501.

Dates
First available in Project Euclid: 19 March 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1174323254

Digital Object Identifier
doi:10.1214/105051606000000745

Mathematical Reviews number (MathSciNet)
MR2308333

Zentralblatt MATH identifier
1125.60112

Subjects
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)

Keywords
Interacting diffusions branching populations local competition extinction ergodic behavior

Citation

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


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