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Evolution of states and mesoscopic scaling for two-component birth-and-death dynamics in continuum


Abstract

Two coupled spatial birth-and-death Markov evolutions on $\mathbb{R}^d$ are obtained as unique weak solutions to the associated Fokker-Planck equations. Such solutions are constructed by its associated sequence of correlation functions satisfying the so-called Ruelle-bound. Using the general scheme of Vlasov scaling we are able to derive a system of non-linear, non-local mesoscopic equations describing the effective density of the particle system. The results are applied to several models of ecology and biology.

Key words: Interacting particle systems, Fokker-Planck equations, Vlasov scaling, mesoscopic scaling.


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Article Information

TitleEvolution of states and mesoscopic scaling for two-component birth-and-death dynamics in continuum
SourceMethods Funct. Anal. Topology, Vol. 22 (2016), no. 4, 346-374
MathSciNet MR3591085
MilestonesReceived 30/08/2016; Revised 01.10.2016
CopyrightThe Author(s) 2016 (CC BY-SA)

Authors Information

Martin Friesen
Department of Mathematics, Bielefeld University, Germany

Oleksandr Kutoviy
Department of Mathematics, Bielefeld University, Germany


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Martin Friesen and Oleksandr Kutoviy, Evolution of states and mesoscopic scaling for two-component birth-and-death dynamics in continuum, Methods Funct. Anal. Topology 22 (2016), no. 4, 346-374.


BibTex

@article {MFAT914,
    AUTHOR = {Friesen, Martin and Kutoviy, Oleksandr},
     TITLE = {Evolution of states and mesoscopic scaling for two-component birth-and-death dynamics in continuum},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {22},
      YEAR = {2016},
    NUMBER = {4},
     PAGES = {346-374},
      ISSN = {1029-3531},
       URL = {http://mfat.imath.kiev.ua/article/?id=914},
}


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