| Título: | Interacting diffusions and trees of excursions: convergence and comparison |
| Autores: | Hutzenthaler, Martin; University of Munich |
| Fecha: | 2012-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: | Peer-reviewed Article |
| Tema: |
Island model; virgin island model; mean field model; McKean-Vlasov limit; extinction; excursion measure; many-demes-limit; propagation of chaos 60K35; 60E15; 92D25 |
| Descripción: | We consider systems of interacting diffusions with local population regulation representing populations on countably many islands. Our main result shows that the total mass process of such a system is bounded above by the total mass process of a tree of excursions with appropriate drift and diffusion coefficients. As a corollary, this entails a sufficient, explicit condition for extinction of the total mass as time tends to infinity. On the way to our comparison result, we establish that systems of interacting diffusions with uniform migration between finitely many islands converge to a tree of excursions as the number of islands tends to infinity. In the special case of logistic branching, this leads to a duality between a tree of excursions and the solution of a McKean-Vlasov equation. |
| Idioma: | Inglés |
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