\(L^p\)-error estimates for numerical schemes for solving certain kinds of backward stochastic differential equations (Q1957154)

\(L^p\) convergence is proved and \(L^p\) error estimates are derived for Crank-Nicolson schemes of Zhao et al. and of Wang et al. for solving the backward stochastic differential eqation \[ y_t= \varphi(W_T)+ \int^T_t f(s, y_s)\,ds- \int^T_t z_s dW_s, \] where \(W_t\) is a standard Brownian motion in \(\mathbb{R}^d\).