A semidiscrete Galerkin scheme for backward stochastic parabolic differential equations

Yanqing  Wang

doi:10.3934/mcrf.2016013

Article Contents

2016, Volume 6, Issue 3: 489-515. Doi: 10.3934/mcrf.2016013

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A semidiscrete Galerkin scheme for backward stochastic parabolic differential equations

Yanqing Wang^1,

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

Received: April 30, 2015

Revised: December 31, 2015

Published: August 2016

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Abstract

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.

Keywords:

Backward stochastic parabolic differential equation,
backward stochastic differential equation,
Galerkin method,
strong convergence.

Mathematics Subject Classification: Primary: 60H15, 65M60; Secondary: 65C30.

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