The mean drift: tailoring the mean field theory of markov processes for real-world applications

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Abstract

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.

Original languageEnglish
Title of host publicationAnalytical and Stochastic Modelling Techniques and Applications
Subtitle of host publication24th International Conference, ASMTA 2017, Newcastle-upon-Tyne, UK, July 10-11, 2017, Proceedings
EditorsN. Thomas, M. Forshaw
Place of PublicationDordrecht
PublisherSpringer
Pages196-211
Number of pages16
ISBN (Electronic)978-3-319-61428-1
ISBN (Print)978-3-319-61427-4
DOIs
Publication statusPublished - 2017
Event24th International Conference on Analytical and Stochastic Modelling Techniques and Applications, (ASMTA 2017), 10-12 July 2017, Newcastle-upon-Tyne, UK - Newcastle-upon-Tyne, United Kingdom
Duration: 10 Jul 201712 Jul 2017
http://asmta.ugent.be/

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10378 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference24th International Conference on Analytical and Stochastic Modelling Techniques and Applications, (ASMTA 2017), 10-12 July 2017, Newcastle-upon-Tyne, UK
Abbreviated titleASMTA 2017
CountryUnited Kingdom
CityNewcastle-upon-Tyne
Period10/07/1712/07/17
Internet address

Keywords

  • Markov chains
  • Mean field approximation
  • Population processes
  • Propagation of chaos

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  • Cite this

    Talebi, M., Groote, J. F., & Linnartz, J. P. M. G. (2017). The mean drift: tailoring the mean field theory of markov processes for real-world applications. In N. Thomas, & M. Forshaw (Eds.), Analytical and Stochastic Modelling Techniques and Applications : 24th International Conference, ASMTA 2017, Newcastle-upon-Tyne, UK, July 10-11, 2017, Proceedings (pp. 196-211). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10378 LNCS). Springer. https://doi.org/10.1007/978-3-319-61428-1_14