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Mean field games in the weak noise limit : A WKB approach to the Fokker–Planck equation

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  • Bonnemain, Thibault
  • Ullmo, Denis

Abstract

Motivated by the study of a Mean Field Game toy model called the “seminar problem”, we consider the Fokker–Planck equation in the small noise regime for a specific drift field. This gives us the opportunity to discuss the application to diffusion problem of the WKB approach “à la Maslov (Maslov and Fedoriuk, 1981)”, making it possible to solve directly the time dependent problem in an especially transparent way.

Suggested Citation

  • Bonnemain, Thibault & Ullmo, Denis, 2019. "Mean field games in the weak noise limit : A WKB approach to the Fokker–Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 310-325.
    • Handle: RePEc:eee:phsmap:v:523:y:2019:i:c:p:310-325
    DOI: 10.1016/j.physa.2019.01.143
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    References listed on IDEAS

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    1. Olivier Guéant & Pierre Louis Lions & Jean-Michel Lasry, 2011. "Mean Field Games and Applications," Post-Print hal-01393103, HAL.
    2. Swiecicki, Igor & Gobron, Thierry & Ullmo, Denis, 2016. "“Phase diagram” of a mean field game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 442(C), pages 467-485.
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