## 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 language | English |
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Title of host publication | Analytical and Stochastic Modelling Techniques and Applications |

Subtitle of host publication | 24th International Conference, ASMTA 2017, Newcastle-upon-Tyne, UK, July 10-11, 2017, Proceedings |

Editors | N. Thomas, M. Forshaw |

Place of Publication | Dordrecht |

Publisher | Springer |

Pages | 196-211 |

Number of pages | 16 |

ISBN (Electronic) | 978-3-319-61428-1 |

ISBN (Print) | 978-3-319-61427-4 |

DOIs | |

Publication status | Published - 2017 |

Event | 24th 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 2017 → 12 Jul 2017 http://asmta.ugent.be/ |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 10378 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 24th International Conference on Analytical and Stochastic Modelling Techniques and Applications, (ASMTA 2017), 10-12 July 2017, Newcastle-upon-Tyne, UK |
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Abbreviated title | ASMTA 2017 |

Country/Territory | United Kingdom |

City | Newcastle-upon-Tyne |

Period | 10/07/17 → 12/07/17 |

Internet address |

## Keywords

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