The Master Field and the Master Equation

René Carmona, François Delarue

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Scopus citations


We introduce the concept of master field within the framework of mean field games with a common noise. We present it as the decoupling field of an infinite dimensional forward-backward system of stochastic partial differential equations characterizing the equilibria. The forward equation is a stochastic Fokker-Planck equation and the backward equation a stochastic Hamilton-Jacobi-Bellman equation. We show that whenever existence and uniqueness of equilibria hold for any initial condition, the master field is a viscosity solution of Lions’ master equation.

Original languageEnglish (US)
Title of host publicationProbability Theory and Stochastic Modelling
PublisherSpringer Nature
Number of pages83
StatePublished - 2018

Publication series

NameProbability Theory and Stochastic Modelling
ISSN (Print)2199-3130
ISSN (Electronic)2199-3149

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Modeling and Simulation
  • Statistics and Probability


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