Electronic Journal of Qualitative Theory of Differential Equations | |
Mean-field approximation of counting processes from a differential equation perspective | |
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