TY - JOUR
T1 - Error Estimates of the Crank-Nicolson Scheme for Solving Backward Stochastic Differential Equations
JO - International Journal of Numerical Analysis and Modeling
VL - 4
SP - 876
EP - 898
PY - 2013
DA - 2013/10
SN - 10
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/601.html
KW - Backward stochastic differential equations, Crank-Nicolson scheme, $\theta$-scheme, error estimate.
AB - <p style="text-align: justify;">In this paper, we study error estimates of a special $\theta$-scheme — the Crank-Nicolson scheme proposed in [25] for solving the backward stochastic differential equation with a general
generator, $-dy_t = f(t, y_t, z_t)dt-z_tdW_t$. We rigorously prove that under some reasonable regularity 
conditions on $\varphi$ and $f$, this scheme is second-order accurate for solving both $y_t$ and $z_t$ when
the errors are measured in the $L^p (p \geq 1)$ norm.</p>