Error estimates of the \(\theta\)-scheme for backward stochastic differential equations
type: Item
instance of: scholarly article
title: Error estimates of the \(\theta\)-scheme for backward stochastic differential equations
zbMATH Open document ID: 1185.60077
author: Weidong Zhao
author: Jinlei Wang
author: Shige Peng
published in: Discrete and Continuous Dynamical Systems. Series B
publication date: 2009-12-16T00:00:00Z
review text: Error bounds are derived for the \(\theta\)-scheme for approximating the solution of the backward stochastic differential equation \[ y_t= \varphi(W_T)+ \int^T_t f(s, y_s)\,ds- \int^T_t z_s\,dW_s, \] where \(W_t\) is standard Brownian motion. It is proved that convergence to \(y_t\) is of second-order when \(\theta={1\over 2}\) and of first-order otherwise, and that convergence to \(z_t\) is of first-order when \(\theta={1\over 2},\,1\). The accuracy of the method and the convergence rates are illustrated by results for three examples whose exact solutions are known.
reviewed by: Melvin D. Lax
Mathematics Subject Classification ID: 60H35
Mathematics Subject Classification ID: 65C20
Mathematics Subject Classification ID: 65C30
zbMATH DE Number: 5648547
zbMATH Keywords: backward stochastic differential equations
zbMATH Keywords: \(\theta\)-scheme
zbMATH Keywords: error estimate
MaRDI profile type: Publication
full work available at URL: dcdsb.2009.12.905
OpenAlex ID: W2117934096
DOI: 10.3934/DCDSB.2009.12.905
description: scientific article; zbMATH DE number 5648547