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

Abstract

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 $O({\tau }^{1/4-\epsilon }+h^{1/2-\epsilon })$ is derived for the natural filtration of the Q-Wiener process.

This work has been accepted for publication in SCIENCE CHINA Mathematics

References in corpus (2)

• A regression-based Monte Carlo method to solve backward stochastic differential equations
• Strong Error Estimates for a Space-Time Discretization of the Linear-Quadratic Control Problem with the Stochastic Heat Equation with Linear Noise

Cited by in corpus (2)

• Convergence of a spatial semi-discretization for a backward semilinear stochastic parabolic equation
• Temporal semi-discretizations of a backward semilinear stochastic evolution equation