Multi-level Monte Carlo method for approximation of distribution functions and an application to AF4

We introduce a multi-level Monte Carlo (MLMC) method for approximation of distribution functions on a compact interval. We establish upper bounds for the error and the cost of suitable multi-level algorithms. As an application we study Asymmetric Flow Field Fractionation (AF4), which is a technique for segregation of two or more particles of submicron size. We apply our MLMC method to study the approximation of the CDF for stopped exit times from the AF4 channel