Implementable coupling of Lévy process and Brownian motion

We provide a simple algorithm for construction of Brownian paths approximating those Lévy process on finite time interval. It requires knowledge the trajectory chosen regular grid and law its endpoint, or ability to simulate from that. This is based reordering increments, it can be applied in recursive manner. establish an upper bound mean squared maximal distance between determine suitable mesh size various asymptotic regimes. The analysis proceeds by reduction comonotonic coupling increments. Applications model risk multilevel Monte Carlo are discussed detail, numerical examples provided.