Project Details
Projekt
Optimal control of McKean-Vlasov stochastic partial differential equations (A10)
Subject Area
Mathematics
Term
since 2024
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 516748464
We aim to systematically develop a variational approach to the control of McKean-Vlasov SPDEs. These SPDEs emerge as driving equations for asymptotic fluctuations in large interacting diffusing particle systems and provide probabilistic representations of certain nonlinear PDEs. Our goal is to derive existence results for optimal controls and optimality conditions, develop an adjoint calculus for the stochastic representation of cost functional gradients, and study the control of McKean-Vlasov equations with singular coefficients. A major application area is exploring the duality between optimal SPDE control and nonlinear stochastic filtering, and the numerical approximation of these systems.
DFG Programme
CRC/Transregios
Applicant Institution
Technische Universität Berlin
Project Heads
Professor Dr. Nicolas Perkowski; Professor Dr. Wilhelm Stannat
