Study On Problems In Implementation Of Multilevel Monte Carlo Methods For β-family Process Based On Wiener-Hopf Factorization

The Wiener-Hopf Monte Carlo method is considered for Levy process. We give the proof of an abstract convergence theorem for the multilevel Monte Carlo method and provide the choice of number of levels and number of paths in each level for the im-plementation of Multilevel Wiener-Hopf Monte Carlo method. Finally, we present an algorithm for sampling from the extrema of β-family process by truncation and the error analysis is given.