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

Dávid Kunszenti-Kovács, L. P. Simon

Research output: Contribution to journalArticle

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

Keywords

  • Exact master equation
  • Fokker-Planck equation
  • Mean-field model

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

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