Noise through an additional variable for mean field games master equation on finite state space
Analysis of PDEs
2024-03-06 v2
Abstract
This paper provides a mathematical study of the well-posedness of master equation on finite state space involving terms modelling common noise. In this setting, the solution of the master equation depends on an additional variable modelling the value of a stochastic process impacting all players. Using technique from viscosity solutions, we give sufficient conditions for the existence of a Lipschitz continuous solution on any time interval. Under some structural assumptions, we are even able to treat cases in which the dynamics of this stochastic process depend on the state of the game.
Keywords
Cite
@article{arxiv.2402.05635,
title = {Noise through an additional variable for mean field games master equation on finite state space},
author = {Charles Bertucci and Charles Meynard},
journal= {arXiv preprint arXiv:2402.05635},
year = {2024}
}