# American Institute of Mathematical Sciences

November  2009, 12(4): 905-924. doi: 10.3934/dcdsb.2009.12.905

## Error estimates of the $\theta$-scheme for backward stochastic differential equations

 1 School of Mathematics, Shandong University, Jinan, Shandong, China, China, China

Received  April 2008 Revised  March 2009 Published  August 2009

In this paper, we study the error estimate of the $\theta$-scheme for the backward stochastic differential equation $y_t=\varphi(W_T)+\int_t^Tf(s,y_s)ds-\int_t^Tz_sdW_s$. We show that this scheme is of first-order convergence in $y$ for general $\theta$. In particular, for the case of $\theta=\frac{1}{2}$ (i.e., the Crank-Nicolson scheme), we prove that this scheme is of second-order convergence in $y$ and first-order in $z$. Some numerical examples are also given to validate our theoretical results.
Citation: Weidong Zhao, Jinlei Wang, Shige Peng. Error estimates of the $\theta$-scheme for backward stochastic differential equations. Discrete & Continuous Dynamical Systems - B, 2009, 12 (4) : 905-924. doi: 10.3934/dcdsb.2009.12.905
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