Numerical analysis of a Neumann boundary control problem with a stochastic parabolic equation

This paper analyzes the discretization of a Neumann boundary control problem with a stochastic parabolic equation, where an additive noise occurs in the Neumann boundary condition. The convergence is established for general filtrations, and the convergence rate $O(τ^{1/4-ε} + h^{1/2-ε})$ is derived for the natural filtration of the Q-Wiener process.

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