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.
|Journal||Electronic Journal of Qualitative Theory of Differential Equations|
|Publication status||Published - Jan 1 2016|
- Exact master equation
- Fokker-Planck equation
- Mean-field model
ASJC Scopus subject areas
- Applied Mathematics