On the simulation of iterated Itô integrals. (Q1879510)

The iterated Itô integrals \[ I_{ij}(t_n, t_n +h)=\int ^{t_n+h}_{t_n}\int _{t_n}^s\,dW_i(u)\,d W_j(s) \] are simulated by different methods simultaneously with \(W_i(t_n+h)-W_i(t_n)\) and \(W_j(t_n+h)-W_j(t_n)\). Mean-square convergence rates for approximations of shot-noise type and asymptotic normality of the remainders are established. A coupling method for the remainder is used to improve the convergence rate. The results are applied to simulation of SDEs.