Convergence and turnpike properties of linear-quadratic mean field control problems with common noise
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866914248872951808 |
|---|---|
| author | Bayraktar, Erhan Jian, Jiamin |
| author_facet | Bayraktar, Erhan Jian, Jiamin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07815 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Convergence and turnpike properties of linear-quadratic mean field control problems with common noise Bayraktar, Erhan Jian, Jiamin Optimization and Control 49N10, 49N90, 93E15, 93E20 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. |
| title | Convergence and turnpike properties of linear-quadratic mean field control problems with common noise |
| topic | Optimization and Control 49N10, 49N90, 93E15, 93E20 |
| url | https://arxiv.org/abs/2601.07815 |