An operator approach to Vlasov scaling for some models of spatial ecology

Authors

  • O. V. Kutoviy Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine
  • Yu. G. Kondratiev Fakultat fur Mathematik, Universitat Bielefeld, 33615 Bielefeld, Germany
  • D. L. Finkelshtein Fakultat fur Mathematik, Universitat Bielefeld, 33615 Bielefeld, Germany  https://orcid.org/0000-0001-7136-9399

DOI:

Keywords:

Continuous systems, spatial birth-and-death processes, individual based models, Vlasov scaling, Vlasov equation, correlation functions

Abstract

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 and convergence to the limiting evolution are shown. The obtained results enable us to derive a non-linear Vlasov-type equation for the density of the limiting system.

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Published

2013-06-25

Issue

Vol. 19 No. 2 (2013)

Section

Articles

How to Cite

Kutoviy, O. V., et al. “An Operator Approach to Vlasov Scaling for Some Models of Spatial Ecology”. Methods of Functional Analysis and Topology, vol. 19, no. 2, June 2013, pp. 108-26, https://zen.imath.kiev.ua/index.php/mfat/article/view/540.