9 citations · 18 across the 9 of their papers we have counts for
9 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 $…
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 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…
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…
Stochastic optimal control in Hilbert spaces: regularity of the value function and optimal synthesis via viscosity solutions
Filippo de Feo, Andrzej Święch, 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…
Neural Network Approximation of Optimal Controls for Stochastic Reaction-Diffusion Equations
Wilhelm Stannat, Alexander Vogler, Lukas Wessels
We present a numerical algorithm that allows the approximation of optimal controls for stochastic reaction-diffusion equations with additive noise by first reducing the problem to…
Peng's Maximum Principle for Stochastic Partial Differential Equations
Wilhelm Stannat, Lukas Wessels
We extend Peng's maximum principle for semilinear stochastic partial differential equations (SPDEs) in one space-dimension with non-convex control domains and control-dependent dif…
Deterministic Control of Stochastic Reaction-Diffusion Equations
Wilhelm Stannat, Lukas Wessels
We consider the control of semilinear stochastic partial differential equations (SPDEs) via deterministic controls. In the case of multiplicative noise, existence of optimal contro…