Operator approach to Vlasov scaling for some models of spatial ecology

Details Operator approach to Vlasov scaling for some models of spatial ecology Operator approach to Vlasov scaling for some models of spatial ecology

2011-04-13

arxiv.org/abs/1104.2418v1

Mathematics

Functional Analysis

28 pages

Scientific paper

We consider Vlasov-type scaling for Markov evolution of birth-and-death type in continuum, which is based on a proper scaling of corresponding Markov generators and has an algorithmic realization in terms of related hierarchical chains of correlation functions equations. The existence of rescaled and limiting evolutions of correlation functions as well as convergence to the limiting evolution are shown. The obtained results enable to derive a non-linear Vlasov-type equation for the density of the limiting system.

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