### Abstract

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.

Original language | English |
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Article number | 75 |

Journal | Electronic Journal of Qualitative Theory of Differential Equations |

Volume | 2016 |

DOIs | |

Publication status | Published - 2016 |

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### ASJC Scopus subject areas

- Applied Mathematics

### Cite this

**Mean-field approximation of counting processes from a differential equation perspective.** / Kunszenti-Kovács, Dávid; Simon, L. P.

Research output: Article

}

TY - JOUR

T1 - Mean-field approximation of counting processes from a differential equation perspective

AU - Kunszenti-Kovács, Dávid

AU - Simon, L. P.

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - Exact master equation

KW - Fokker-Planck equation

KW - Mean-field model

UR - http://www.scopus.com/inward/record.url?scp=84987817218&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84987817218&partnerID=8YFLogxK

U2 - 10.14232/ejqtde.2016.1.75

DO - 10.14232/ejqtde.2016.1.75

M3 - Article

AN - SCOPUS:84987817218

VL - 2016

JO - Electronic Journal of Qualitative Theory of Differential Equations

JF - Electronic Journal of Qualitative Theory of Differential Equations

SN - 1417-3875

M1 - 75

ER -