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

Binjie Li; Xiaoping Xie

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arXiv · 2105.10130

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

Binjie Li·Xiaoping Xie

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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.

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Binjie Li, Xiaoping Xie. 2021-05-21. Convergence of a spatial semi-discretization for a backward semilinear stochastic parabolic equation. https://arxiv.org/abs/2105.10130

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