Mean field games with common noise and degenerate idiosyncratic noise
Analysis of PDEs
2025-01-14 v2 Probability
Abstract
We study the forward-backward system of stochastic partial differential equations describing a mean field game for a large population of small players subject to both idiosyncratic and common noise. The unique feature of the problem is that the idiosyncratic noise coefficient may be degenerate, so that the system does not admit smooth solutions in general. We develop a new notion of weak solutions for backward stochastic Hamilton-Jacobi-Bellman equations, and use this to build probabilistically weak solutions of the mean field game system.
Keywords
Cite
@article{arxiv.2207.10209,
title = {Mean field games with common noise and degenerate idiosyncratic noise},
author = {Pierre Cardaliaguet and Benjamin Seeger and Panagiotis Souganidis},
journal= {arXiv preprint arXiv:2207.10209},
year = {2025}
}
Comments
revised version, expanded details on stochastic processes in the space of distributions. To appear in AAP