LpLp-error estimates for numerical schemes for solving certain kinds of backward stochastic differential equations

In this paper, we study LpLp-error estimates for a scheme proposed by Zhao et al. (2006) for solving the backward stochastic differential equations −dyt=f(t,yt)dt−ztdWt. We prove that this scheme is of second-order convergence for solving for ytyt and of first-order convergence for solving for ztzt in LpLp norm. And we also prove that the Crank–Nicolson scheme proposed by Wang et al. (2009) is second-order convergent for solving for both ytyt and ztzt in LpLp norm.