Open Access

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

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.

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

Article Information

 Title An operator approach to Vlasov scaling for some models of spatial ecology Source Methods Funct. Anal. Topology, Vol. 19 (2013), no. 2, 108-126 MathSciNet MR3098491 zbMATH 1289.92068 Milestones Received 02/11/2012; Revised 14/01/2013 Copyright The Author(s) 2013 (CC BY-SA)

Authors Information

D. Finkelshtein
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

Yu. Kondratiev
Fakultat fur Mathematik, Universitat Bielefeld, 33615 Bielefeld, Germany

O. Kutoviy
Fakultat fur Mathematik, Universitat Bielefeld, 33615 Bielefeld, Germany

Citation Example

D. Finkelshtein, Yu. Kondratiev, and O. Kutoviy, An operator approach to Vlasov scaling for some models of spatial ecology, Methods Funct. Anal. Topology 19 (2013), no. 2, 108-126.

BibTex

@article {MFAT667,
AUTHOR = {Finkelshtein, D. and Kondratiev, Yu. and Kutoviy, O.},
TITLE = {An operator approach to Vlasov scaling for some models of spatial ecology},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {19},
YEAR = {2013},
NUMBER = {2},
PAGES = {108-126},
ISSN = {1029-3531},
MRNUMBER = {MR3098491},
ZBLNUMBER = {1289.92068},
URL = {http://mfat.imath.kiev.ua/article/?id=667},
}