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

2021/05/21 by Binjie Li, Li, Binjie, Xiaoping Xie +1
Computer Science · Economics, Econometrics and Finance · Engineering · #49M25 #60H35 #65C30 #65K10 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2105.10130

openalex publication_date 2021/05/21 · openalex created_date 2021/06/07 · openalex updated_date 2026/07/28

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.

Citations

• Conjugate convex functions in optimal stochastic control
• Galerkin Finite Element Methods for Stochastic Parabolic Partial Differential Equations
• Optimal Feedback for Stochastic Linear Quadratic Control and Backward Stochastic Riccati Equations in Infinite Dimensions
• Strong and Weak Convergence Rates of a Spatial Approximation for Stochastic Partial Differential Equation with One-sided Lipschitz Coefficient
• Strong Error Estimates for a Space-Time Discretization of the Linear-Quadratic Control Problem with the Stochastic Heat Equation with Linear Noise
• Analysis of a discretization of a distributed control problem with a stochastic evolution equation

Related

• Temporal semi-discretizations of a backward semilinear stochastic evolution equation
• A Semidiscrete Galerkin Scheme for Backward Stochastic Parabolic Differential Equations
• 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
• Strong convergence of the backward Euler approximation for the finite element discretization of semilinear parabolic SPDEs with non-global Lipschitz drift driven by additive noise
• Null controllability for stochastic fourth order semi-discrete parabolic equations