Mean-field approximation of counting processes from a differential equation perspective

Electronic Journal of Qualitative Theory of Differential Equations

Péter Simon¹  Dávid Kunszenti-Kovács² 

[1] Eötvös Loránd University, Budapest, Hungary;MTA Alfréd Rényi Institute of Mathematics, Budapest, Hungary and Numerical Analysis and Large Networks Research Group Hungarian Academy of Sciences, Hungary;

关键词: mean-field model;    exact master equation;    fokker–planck equation;   

DOI  :  10.14232/ejqtde.2016.1.75

来源: DOAJ

【 摘 要 】

Deterministic limit of a class of continuous time Markov chains is considered based purely on differential equation techniques. Starting from the linear system of master equations, ordinary differential equations for the moments and a partial differential equation, called Fokker–Planck equation, for the distribution is derived. Introducing closures at the level of the second and third moments, mean-field approximations are introduced. The accuracy of the mean-field approximations and the Fokker–Planck equation is investigated by using two differential equation-based and an operator semigroup-based approach.

【 授权许可】

Unknown