Ergodic behavior of locally regulated branching populations

By BY M. Hutzenthaler, Anton Wakolbinger, J. Wolfgang. 2005

49 citations recorded by the source corpus.

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 towards an upper invariant measure from a suitable class of initial distributions. It follows from recent work of A. Etheridge that this upper invariant measure is non-trivial 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.

Subfields: Genetics, Mathematical Physics, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/90a45fdb1b9ad7303f102995adb7a549c4f3f035

Citations in the corpus

• Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients (2010, unknown): “This is particularly unfortunate as SDEs with superlinearly growing coefficients are quite important in applications (see, e.g., [2, 8, 17, 18, 23, 30, 33]).”
• Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients (2009, unknown): “However, it features the following self-duality for all t ∈ [0 , T ] and all x, y ∈ [0 , ∞ ) where E x refers to the starting point X 0 = x , see Hutzenthaler & Wakolbinger (2007).”