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

Dávid Kunszenti-Kovács, L. P. Simon

Research output: Article

1 Citation (Scopus)

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 languageEnglish
Article number75
JournalElectronic Journal of Qualitative Theory of Differential Equations
Volume2016
DOIs
Publication statusPublished - 2016

Fingerprint

Fokker Planck equation
Counting Process
Mean-field Approximation
Fokker-Planck Equation
Differential equations
Differential equation
Operator Semigroups
Moment
Continuous-time Markov Chain
Master Equation
Ordinary differential equations
Markov processes
Partial differential equations
Linear systems
Mathematical operators
Closure
Ordinary differential equation
Partial differential equation
Linear Systems
Class

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

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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.

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