Introduction: Main Models and LLN Methodology

  • Vassili N. KolokoltsovEmail author
  • Oleg A. Malafeyev
Part of the Springer Series in Operations Research and Financial Engineering book series (ORFE)


The first sections of this chapter are devoted to a brief introduction to our basic model of controlled mean-field interacting particle systems, its principal features in the framework of pressure and resistance, and to the fundamental paradigm of the scaling limit (dynamic law of large numbers), allowing one to reduce the analysis of these Markov chains with exponentially large state spaces to a low-dimensional dynamic system expressed in terms of simple ordinary differential equations (ODEs), so called kinetic equations.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of WarwickCoventryUK
  2. 2.Faculty of Applied Mathematics and Control ProcessesSaint Petersburg State UniversitySaint PetersburgRussia

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