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2012 Interacting diffusions and trees of excursions: convergence and comparison
Martin Hutzenthaler
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Electron. J. Probab. 17: 1-49 (2012). DOI: 10.1214/EJP.v17-2278


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.


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Martin Hutzenthaler. "Interacting diffusions and trees of excursions: convergence and comparison." Electron. J. Probab. 17 1 - 49, 2012.


Accepted: 28 August 2012; Published: 2012
First available in Project Euclid: 4 June 2016

zbMATH: 1284.60169
MathSciNet: MR2968678
Digital Object Identifier: 10.1214/EJP.v17-2278

Primary: 60K35
Secondary: 60E15 , 92D25

Keywords: Excursion measure , extinction , Island model , many-demes-limit , McKean-Vlasov limit , mean field model , propagation of chaos , Virgin Island Model


Vol.17 • 2012
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