부산대학교 도서관

In this paper, we recall the result about the strong convergence rate of the Ninomiya-Victoir scheme and the properties of the multilevel Monte Carlo estimators involving this scheme that we introduced and studied in [2]. We are also interested in the error introduced by discretizing the ordinary differential equations involved in the Ninomiya-Victoir scheme. We prove that this error converges with strong order 2 when an explicit Runge-Kutta method with order 4 (resp. 2) is used for the ODEs corresponding to the Brownian (resp. Stratonovich drift) vector fields. We thus relax the order 5 needed in [11] for the Brownian ODEs to obtain the same order of strong convergence. Moreover, the properties of our multilevel Monte-Carlo estimators are preserved when these Runge-Kutta methods are used.