The Mean Drift: Tailoring the Mean Field Theory of Markov Processes for Real-World Applications

  • Mahmoud TalebiEmail author
  • Jan Friso Groote
  • Jean-Paul M. G. Linnartz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10378)


The statement of the mean field approximation theorem in the mean field theory of Markov processes particularly targets the behaviour of population processes with an unbounded number of agents. However, in most real-world engineering applications one faces the problem of analysing middle-sized systems in which the number of agents is bounded. In this paper we build on previous work in this area and introduce the mean drift. We present the concept of population processes and the conditions under which the approximation theorems apply, and then show how the mean drift can be linked to observations which follow from the propagation of chaos. We then use the mean drift to construct a new set of ordinary differential equations which address the analysis of population processes with an arbitrary size.


Markov chains Population processes Mean field approximation Propagation of chaos 



The research from DEWI project ( leading to these results has received funding from the ARTEMIS Joint Undertaking under grant agreement No. 621353.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Mahmoud Talebi
    • 1
    Email author
  • Jan Friso Groote
    • 1
  • Jean-Paul M. G. Linnartz
    • 2
  1. 1.Department of Mathematics and Computer ScienceEindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.Department of Electrical EngineeringEindhoven University of TechnologyEindhovenThe Netherlands

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