Convergence and turnpike properties of linear-quadratic mean field control problems with common noise
Abstract
We investigate convergence and turnpike properties for linear-quadratic mean field control problems with common noise. Within a unified framework, we analyze a finite-horizon social optimization problem, its mean field control limit, and the corresponding ergodic mean field control problem. The finite-horizon problems are characterized by coupled Riccati differential equations, whereas the ergodic problem is addressed via a Bellman equation on the Wasserstein space, which reduces to a system of stabilizing algebraic Riccati equations. By deriving estimates for these Riccati systems, we establish a turnpike property for the finite-horizon mean field control problem and obtain quantitative convergence results from the social optimization problem to its mean field limit and the associated ergodic control problem.
Keywords
Cite
@article{arxiv.2601.07815,
title = {Convergence and turnpike properties of linear-quadratic mean field control problems with common noise},
author = {Erhan Bayraktar and Jiamin Jian},
journal= {arXiv preprint arXiv:2601.07815},
year = {2026}
}