Discretization Error of Stochastic Iterated Integrals

In this paper, the weak convergence about the discretization error of stochastic iterated integrals in the Skorohod sense are studied, while the integrands and integrators of iterated integrals are supposed to be semimartingales with jumps. We explored the rate of convergence of its approximation based on the asymptotic behaviors of the associated normalized error and obtained that the rate is $1/n$ when the driving process is semimartingale with a nonvanishing continuous martingale component. As an application, we also studied the discretization of the Dol\'eans-Dade exponential.