@inbook{6acefd50c2e84a2a9e8c80fd102d3a02,
title = "The Master Field and the Master Equation",
abstract = "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{\textquoteright} master equation.",
author = "Ren{\'e} Carmona and Fran{\c c}ois Delarue",
note = "Publisher Copyright: {\textcopyright} 2018, Springer International Publishing AG.",
year = "2018",
doi = "10.1007/978-3-319-56436-4_4",
language = "English (US)",
series = "Probability Theory and Stochastic Modelling",
publisher = "Springer Nature",
pages = "239--321",
booktitle = "Probability Theory and Stochastic Modelling",
address = "United States",
}