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math.PR2024
Non-negative Martingale Solutions to the Stochastic Porous Medium Equation with Sticky Behavior
Ben Hambly, Dörte Kreher, Konstantins Starovoitovs
We construct non-negative martingale solutions to the stochastic porous medium equation in one dimension with homogeneous Dirichlet boundary conditions which exhibit a type of stic…
math.OC2024
Optimal Control of the Nonlinear Stochastic Fokker--Planck Equation
Ben Hambly, Philipp Jettkant
We consider a control problem for the nonlinear stochastic Fokker--Planck equation. This equation describes the evolution of the distribution of nonlocally interacting particles af…