ABSTRACT
This chapter discusses the statistical error that appears in the simulation of stochastic differential equations, in connection with the discretization step that is chosen for the process approximation. It provides guidance for a proper choice of the number of trajectories and the time step. Instead of allocating all the effort to the calculation by the Euler scheme with a small time step and with a large number of simulations the multi-level approach will rather progressively spread the effort over the Euler schemes with a geometrically decreasing step, for example, twice smaller at each next level. The main idea is to take advantage of the fact that at coarse levels the error is large but the computational cost is small, and the error gradually decreases while the computational cost increases.
