Kunszenti-Kovács, Dávid; Simon, Péter Mean-field approximation of counting processes from a differential equation perspective. (English) Zbl 1389.35301 Electron. J. Qual. Theory Differ. Equ. 2016, Paper No. 75, 17 p. (2016). Summary: 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. Cited in 1 Document MSC: 35Q84 Fokker-Planck equations 47D06 One-parameter semigroups and linear evolution equations 47N40 Applications of operator theory in numerical analysis 60J28 Applications of continuous-time Markov processes on discrete state spaces 65C40 Numerical analysis or methods applied to Markov chains Keywords:mean-field model; exact master equation; Fokker-Planck equation PDFBibTeX XMLCite \textit{D. Kunszenti-Kovács} and \textit{P. Simon}, Electron. J. Qual. Theory Differ. Equ. 2016, Paper No. 75, 17 p. (2016; Zbl 1389.35301) Full Text: DOI