Electronic Journal of Probability
- Electron. J. Probab.
- Volume 17 (2012), paper no. 71, 49 pp.
Interacting diffusions and trees of excursions: convergence and comparison
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.
Electron. J. Probab., Volume 17 (2012), paper no. 71, 49 pp.
Accepted: 28 August 2012
First available in Project Euclid: 4 June 2016
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: 60E15: Inequalities; stochastic orderings 92D25: Population dynamics (general)
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Hutzenthaler, Martin. Interacting diffusions and trees of excursions: convergence and comparison. Electron. J. Probab. 17 (2012), paper no. 71, 49 pp. doi:10.1214/EJP.v17-2278. https://projecteuclid.org/euclid.ejp/1465062393