6 papers
On a stochastic phase-field model of cell motility with singular diffusion
Amjad Saef, Wilhelm Stannat
We study existence of solutions in the variational sense for a class of stochastic phase-field models describing moving boundary problems. The models consist of stochastic reaction…
Peng's Maximum Principle for McKean-Vlasov Stochastic Differential Equations with Common Noise
Johan Benedikt Spille, Wilhelm Stannat
We study a stochastic optimal control problem for McKean-Vlasov stochastic differential equations (SDEs) with common noise, where the dynamics depend on the conditional law of the…
A Novel Approach to Peng's Maximum Principle for McKean-Vlasov Stochastic Differential Equations
Johan Benedikt Spille, Wilhelm Stannat
We present a novel approach to the proof of Peng's maximum principle for McKean-Vlasov stochastic differential equations (SDE). The main step is the introduction of a third adjoint…
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…
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…
Parameter dependent rough SDEs with applications to rough PDEs
Fabio Bugini, Peter K. Friz, Wilhelm Stannat
Rough stochastic differential equations (rough SDEs), recently introduced by Friz, Hocquet and Lê in arXiv:2106.10340, have emerged as a versatile tool to study "doubly" SDEs unde…