# Advances in Probability and Mathematical StatisticsApproximation and Mean Field Control of Systems of Large Populations

Advances in Probability and Mathematical Statistics: Approximation and Mean Field Control of... [We deal with a class of discrete-time stochastic controlled systems composed by a large population of N interacting individuals. Given that N is large and the cost function is possibly unbounded, the problem is studied by means of a limit model ℳ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal {M}$$ \end{document}, known as the mean field model, which is obtained as limit as N →∞ of the model ℳN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal {M}_N$$ \end{document} corresponding to the system of N individuals in combination with an approximate algorithm for the cost function.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# Advances in Probability and Mathematical StatisticsApproximation and Mean Field Control of Systems of Large Populations

Part of the Progress in Probability Book Series (volume 79)
Editors: Hernández‐Hernández, Daniel; Leonardi, Florencia; Mena, Ramsés H.; Pardo Millán, Juan Carlos
19 pages

# References (9)

Publisher
Springer International Publishing
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
ISBN
978-3-030-85324-2
Pages
103 –122
DOI
10.1007/978-3-030-85325-9_7
Publisher site
See Chapter on Publisher Site

### Abstract

[We deal with a class of discrete-time stochastic controlled systems composed by a large population of N interacting individuals. Given that N is large and the cost function is possibly unbounded, the problem is studied by means of a limit model ℳ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal {M}$$ \end{document}, known as the mean field model, which is obtained as limit as N →∞ of the model ℳN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal {M}_N$$ \end{document} corresponding to the system of N individuals in combination with an approximate algorithm for the cost function.]

Published: Aug 5, 2021

Keywords: Systems of interacting individuals; Mean field theory; Approximation algorithm; Discounted criterion

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