Error estimates of the \(\theta\)-scheme for backward stochastic differential equations
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.
backward stochastic differential equations
scientific article; zbMATH DE number 5648547