Open Access

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.

Article Information

 Title Evolution of states and mesoscopic scaling for two-component birth-and-death dynamics in continuum Source Methods Funct. Anal. Topology, Vol. 22 (2016), no. 4, 346-374 Milestones Received 30/08/2016; Revised 01.10.2016 Copyright The Author(s) 2016 (CC BY-SA)

Authors Information

Martin Friesen
Department of Mathematics, Bielefeld University, Germany

Oleksandr Kutoviy
Department of Mathematics, Bielefeld University, Germany

Citation Example

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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