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math.PR2025
Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations
Johan Benedikt Spille, Wilhelm Stannat
We consider the stochastic control of a semi-linear stochastic partial differential equations (SPDE) of McKean-Vlasov type. Based on a recent novel approach to the Lions derivative…
math.PR2025
Nonlinear rough Fokker-Planck equations
Fabio Bugini, Peter K. Friz, Wilhelm Stannat
McKean-Vlasov SDEs describe systems where the dynamics depend on the law of the process. The corresponding Fokker-Planck equation is a nonlinear, nonlocal PDE for the corresponding…