Pith. sign in

REVIEW 2 cited by

On Mean Field Games in Infinite Dimension

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2411.14604 v3 pith:5PVGCX5J submitted 2024-11-21 math.AP math.OC

Salvatore Federico , Fausto Gozzi , Andrzej Święch This is my paper · ORCID
classification math.APmath.OC
keywords equationsystemsolutionsconditionsfieldgamesinfiniteinterpreted
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

We study a Mean Field Games (MFG) system in a real, separable infinite dimensional Hilbert space. The system consists of a second order parabolic type equation, called Hamilton-Jacobi-Bellman (HJB) equation in the paper, coupled with a nonlinear Fokker-Planck (FP) equation. Both equations contain a Kolmogorov operator. Solutions to the HJB equation are interpreted in the mild solution sense and solutions to the FP equation are interpreted in an appropriate weak sense. We prove well-posedness of the considered MFG system under certain conditions. The existence of a solution to the MFG system is proved using Tikhonov's fixed point theorem in a proper space. Uniqueness of solutions is obtained under typical separability and Lasry-Lions type monotonicity conditions.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Infinite-Dimensional LQ Mean Field Games with Common Noise: Small and Arbitrary Finite Time Horizons

    math.OC 2026-01 conditional novelty 6.0 of 10

    Infinite-dimensional linear-quadratic mean field games with common noise have unique equilibria for small time horizons and, under deterministic common-noise diffusion, for arbitrary finite time horizons.

  2. Linear-quadratic stochastic nonzero-sum differential games between graphon teams

    math.OC 2025-06 conditional novelty 6.0 of 10

    For a linear-quadratic nonzero-sum game between two graphon teams, the paper derives a Nash equilibrium from coupled Riccati equations and proves existence for sufficiently small cross-team coupling.

Pith tools