Derivation of mean-field equations for stochastic particle systems

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:129

Article

Grosskinsky, Stefan¹  Jatuviriyapornchai, Watthanan^2,3 

[1] Univ Warwick, Math Inst, Coventry CV4 7AL, W Midlands, England

[2] Mahidol Univ, Fac Sci, Dept Math, Bangkok 10400, Thailand

[3] Commiss Higher Educ, Ctr Excellence Math, Bangkok 10400, Thailand

关键词: Mean-field equations;    Misanthrope processes;    Non-linear birth death chain;    condensation;   

DOI  :  10.1016/j.spa.2018.05.006

来源: Elsevier

【 摘 要 】

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. (C) 2018 Published by Elsevier B.V.

【 授权许可】

Free