[HTML][HTML] Existence of a solution to an equation arising from the theory of mean field games

W Gangbo, A Święch - Journal of Differential equations, 2015 - Elsevier
We construct a small time strong solution to a nonlocal Hamilton–Jacobi equation (1.1)
introduced in [48], the so-called master equation, originating from the theory of Mean Field …

Global Well‐Posedness of Master Equations for Deterministic Displacement Convex Potential Mean Field Games

W Gangbo, AR Mészáros - Communications on Pure and …, 2022 - Wiley Online Library
This manuscript constructs global in time solutions to master equations for potential mean
field games. The study concerns a class of Lagrangians and initial data functions that are …

Master Bellman equation in the Wasserstein space: Uniqueness of viscosity solutions

A Cosso, F Gozzi, I Kharroubi, H Pham… - Transactions of the …, 2024 - ams.org
We study the Bellman equation in the Wasserstein space arising in the study of mean field
control problems, namely stochastic optimal control problems for McKean-Vlasov diffusion …

Nonconvex interactions in mean-field spin glasses

JC Mourrat - Probability and Mathematical Physics, 2021 - msp.org
We propose a conjecture for the limit free energy of mean-field spin glasses with a bipartite
structure, and show that the conjectured limit is an upper bound. The conjectured limit is …

Finite Dimensional Approximations of Hamilton--Jacobi--Bellman Equations in Spaces of Probability Measures

W Gangbo, S Mayorga, A Swiech - SIAM Journal on Mathematical Analysis, 2021 - SIAM
We prove that viscosity solutions of Hamilton--Jacobi--Bellman (HJB) equations,
corresponding either to deterministic optimal control problems for systems of n particles or to …

[HTML][HTML] On a class of first order Hamilton–Jacobi equations in metric spaces

L Ambrosio, J Feng - Journal of Differential Equations, 2014 - Elsevier
We establish well-posedness of a class of first order Hamilton–Jacobi equation in geodesic
metric spaces. The result is then applied to solve a Hamilton–Jacobi equation in the …

Finite dimensional approximations of hamilton–jacobi–bellman equations for stochastic particle systems with common noise

S Mayorga, A Święch - SIAM Journal on Control and Optimization, 2023 - SIAM
This paper is a continuation of the program started in [W. Gangbo, S. Mayorga, and A.
Święch, SIAM J. Math. Anal., 53 (2021), pp. 1320–1356]. We consider stochastic optimal …

Mean field games systems under displacement monotonicity

AR Mészáros, C Mou - SIAM Journal on Mathematical Analysis, 2024 - SIAM
In this note we prove the uniqueness of solutions to a class of mean field games systems
subject to possibly degenerate individual noise. Our results hold true for arbitrary long time …

Metric viscosity solutions of Hamilton–Jacobi equations depending on local slopes

W Gangbo, A Święch - Calculus of Variations and Partial Differential …, 2015 - Springer
We continue the study of viscosity solutions of Hamilton–Jacobi equations in metric spaces
initiated in [37]. We present a more complete account of the theory of metric viscosity …

The Parisi formula is a Hamilton–Jacobi equation in Wasserstein space

JC Mourrat - Canadian Journal of Mathematics, 2022 - cambridge.org
The Parisi formula is a self-contained description of the infinite-volume limit of the free
energy of mean-field spin glass models. We showthat this quantity can be recast as the …