Central Limit Theorem for Irregular Discretization Scheme of Multilevel Monte Carlo Method

In this paper, we study the asymptotic error distribution for a two-level irregular discretization scheme of the solution to the stochastic differential equations (SDE for short) driven by a continuous semimartingale and obtain a central limit theorem for the error processes with the rate $\sqrt{n}$. As an application, in the spirit of the result of Ben Alaya and Kebaier, we get a central limit theorem of the Linderberg-Feller type for the irregular discretization scheme of the multilevel Monte Carlo method.