6 papers
Mean Field Games in Hilbert Spaces with Degenerate Diffusion: A Viscosity Solution Approach
Andrzej ÅwiÄch, 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 $…
Peng's Maximum Principle for Stochastic Delay Differential Equations of Mean-Field Type
Giuseppina Guatteri, Federica Masiero, Lukas Wessels
We extend Peng's maximum principle to the case of stochastic delay differential equations of mean-field type. More precisely, the coefficients of our control problem depend on the…
Stochastic Optimal Control of Interacting Particle Systems in Hilbert Spaces and Applications
Filippo de Feo, Fausto Gozzi, Andrzej ÅwiÄch +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…
Finite Dimensional Projections of HJB Equations in the Wasserstein Space
Andrzej ÅwiÄch, Lukas Wessels
This paper continues the study of controlled interacting particle systems with common noise started in [W. Gangbo, S. Mayorga and A. ÅwiÄch, SIAM J. Math. Anal. 53 (2021), no. 2,…
Stochastic optimal control in Hilbert spaces: regularity of the value function and optimal synthesis via viscosity solutions
Filippo de Feo, Andrzej ÅwiÄch, Lukas Wessels
We study optimal control problems governed by abstract infinite dimensional stochastic differential equations using the dynamic programming approach. In the first part, we prove Li…
Semilinear Feynman-Kac Formulae for -Continuous Viscosity Solutions
Lukas Wessels
We prove the existence of a -continuous viscosity solution for a class of infinite dimensional semilinear partial differential equations (PDEs) using probabilistic methods. Our…