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Mean-field approximation of counting processes from a differential equation perspective. (English) Zbl 1389.35301

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.

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
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