Discretization error of irregular sampling approximations of stochastic integrals

This paper studies the limit distributions for discretization error of irregular sampling approximations of stochastic integral. The irregular sampling approximation was first presented in Hayashi et al.[3], which was more general than the sampling approximation in Lindberg and Rootz′en [10]. As applications, we derive the asymptotic distribution of hedging error and the Euler scheme of stochastic differential equation respectively.