Publication: Derivation of mean-field equations for stochastic particle systems
Issued Date
2019-04-01
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ISSN
03044149
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2-s2.0-85047818792
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Mahidol University
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SCOPUS
Bibliographic Citation
Stochastic Processes and their Applications. Vol.129, No.4 (2019), 1455-1475
Suggested Citation
Stefan Grosskinsky, Watthanan Jatuviriyapornchai Derivation of mean-field equations for stochastic particle systems. Stochastic Processes and their Applications. Vol.129, No.4 (2019), 1455-1475. doi:10.1016/j.spa.2018.05.006 Retrieved from: https://repository.li.mahidol.ac.th/handle/20.500.14594/51227
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Title
Derivation of mean-field equations for stochastic particle systems
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Abstract
© 2018 We study stochastic particle systems on a complete graph and derive effective mean-field rate equations in the limit of diverging system size, which are also known from cluster aggregation models. We establish the propagation of chaos under generic growth conditions on particle jump rates, and the limit provides a master equation for the single site dynamics of the particle system, which is a non-linear birth death chain. Conservation of mass in the particle system leads to conservation of the first moment for the limit dynamics, and to non-uniqueness of stationary distributions. Our findings are consistent with recent results on exchange driven growth, and provide a connection between the well studied phenomena of gelation and condensation.