# American Institute of Mathematical Sciences

September  2016, 6(3): 489-515. doi: 10.3934/mcrf.2016013

## A semidiscrete Galerkin scheme for backward stochastic parabolic differential equations

 1 School of Mathematics and Statistics, Southwest University, Chongqing 400715, China

Received  May 2015 Revised  January 2016 Published  August 2016

In this paper, we present a numerical scheme to solve the initial-boundary value problem for backward stochastic partial differential equations of parabolic type. Based on the Galerkin method, we approximate the original equation by a family of backward stochastic differential equations (BSDEs, for short), and then solve these BSDEs by the time discretization. Combining the truncation with respect to the spatial variable and the backward Euler method on time variable, we obtain the global $L^2$ error estimate.
Citation: Yanqing Wang. A semidiscrete Galerkin scheme for backward stochastic parabolic differential equations. Mathematical Control & Related Fields, 2016, 6 (3) : 489-515. doi: 10.3934/mcrf.2016013
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