Convergence of a spatial semi-discretization for a backward semilinear stochastic parabolic equation

Abstract

This paper studies the convergence of a spatial semi-discretization for a backward semilinear stochastic parabolic equation. The filtration is general, and the spatial semi-discretization uses the standard continuous piecewise linear element method. Firstly, higher regularity of the solution to the continuous equation is derived. Secondly, the first-order spatial accuracy is derived for the spatial semi-discretization. Thirdly, an application of the theoretical result to a stochastic linear quadratic control problem is presented.

References in corpus (4)

• Strong Error Estimates for a Space-Time Discretization of the Linear-Quadratic Control Problem with the Stochastic Heat Equation with Linear Noise
• Strong Rates of Convergence for Space-Time Discretization of the Backward Stochastic Heat Equation, and of a Linear-Quadratic Control Problem for the Stochastic Heat Equation
• Numerical analysis of a Neumann boundary control problem with a stochastic parabolic equation
• Analysis of a discretization of a distributed control problem with a stochastic evolution equation

Cited by in corpus (1)

• Temporal semi-discretizations of a backward semilinear stochastic evolution equation