6 papers
Mean Field Games in Hilbert Spaces with Degenerate Diffusion: A Viscosity Solution Approach
Andrzej Święch, Lukas Wessels
We study a degenerate second order mean field game (MFG) system in a Hilbert space which couples a Fokker--Planck equation describing the evolution of probability measures on $…
Stochastic Optimal Control of Interacting Particle Systems in Hilbert Spaces and Applications
Filippo de Feo, Fausto Gozzi, Andrzej Święch +1
Optimal control of interacting particles governed by stochastic evolution equations in Hilbert spaces is an open area of research. Such systems naturally arise in formulations wher…
On Mean Field Games in Infinite Dimension
Salvatore Federico, Fausto Gozzi, Andrzej Święch
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-Jac…
Finite Dimensional Projections of HJB Equations in the Wasserstein Space
Andrzej Święch, Lukas Wessels
This paper continues the study of controlled interacting particle systems with common noise started in [W. Gangbo, S. Mayorga and A. Święch, SIAM J. Math. Anal. 53 (2021), no. 2, 1…
Optimal control of stochastic delay differential equations: Optimal feedback controls
Filippo de Feo, Andrzej Święch
In this manuscript, we study optimal control problems for stochastic delay differential equations using the dynamic programming approach in Hilbert spaces via viscosity solutions o…
Viscosity solutions to an initial value problem for a Hamilton--Jacobi equation with a degenerate Hamiltonian occurring in the dynamics of peakons
Tomasz Cieślak, Jakub Siemianowski, Andrzej Święch
We consider an initial value problem for a Hamilton--Jacobi equation with a quadratic and degenerate Hamiltonian. Our Hamiltonian comes from the dynamics of -peakon in the Camas…