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Deterministic approximation of a stochastic metapopulation model

Part of: Infinite-dimensional dissipative dynamical systems Probability theory on algebraic and topological structures Markov processes Differential equations in abstract spaces

Published online by Cambridge University Press:  01 July 2016

Francesca Arrigoni
Francesca Arrigoni*
Affiliation:
University of Trento
*
∗ Postal address: Department of Mathematics, University of Trento, via Sommarive 14, 38050 Povo, Trento, Italy. Email address: arrigoni@science.unitn.it
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Abstract

We analyse the limit behaviour of a stochastic structured metapopulation model as the number of its patches goes to infinity. The sequence of probability measures associated with the random process, whose components are the proportions of patches with different number of individuals, is tight. The limit of every convergent subsequence satisfies an infinite system of ordinary differential equations. The existence and the uniqueness of the solution are shown by semigroup methods, so that the whole random process converges weakly to the solution of the system.

Keywords

MetapopulationMarkov chainweak convergence

MSC classification

Primary: 37L05: General theory, nonlinear semigroups, evolution equations 92D40: Ecology 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60B12: Limit theorems for vector-valued random variables (infinite-dimensional case) 34G20: Nonlinear equations

Information

Type
General Applied Probability
Information
Advances in Applied Probability , Volume 35 , Issue 3 , September 2003 , pp. 691 - 720
Copyright
Copyright © Applied Probability Trust 2003 

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